Line: 1 to 1 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||||||

Line: 33 to 33 | ||||||||||||

| ||||||||||||

Changed: | ||||||||||||

< < |
| |||||||||||

> > |
| |||||||||||

| ||||||||||||

Added: | ||||||||||||

> > |
| |||||||||||

## Relevant papers covered (so far & soon) |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 37 to 37 | ||||||||

| ||||||||

Added: | ||||||||

> > |
| |||||||

## Relevant papers covered (so far & soon) |

Line: 1 to 1 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | |||||||||||

Line: 31 to 31 | |||||||||||

| |||||||||||

Deleted: | |||||||||||

< < |
| ||||||||||

| |||||||||||

Deleted: | |||||||||||

< < |
| ||||||||||

| |||||||||||

Changed: | |||||||||||

< < |
| ||||||||||

> > |
| ||||||||||

## Relevant papers covered (so far & soon) |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 41 to 41 | ||||||||

| ||||||||

Changed: | ||||||||

< < |
| |||||||

> > |
| |||||||

## Relevant papers covered (so far & soon) | ||||||||

Line: 68 to 69 | ||||||||

Hausdorff dimension of planar Brownian motion | ||||||||

Changed: | ||||||||

< < | Gregory F. Lawler, Oded Schramm, and Wendelin Werner, The dimension of the planar Brownian frontier is $4/3$. Math. Res. Lett. 8, 401-411 (2001). MathJournals | |||||||

> > | Gregory F. Lawler, Oded Schramm, and Wendelin Werner, The dimension of the planar Brownian frontier is $4/3$. Math. Res. Lett. 8, 401-411 (2001). MathJournals (see also references within) | |||||||

Changed: | ||||||||

< < | (see also references within) | |||||||

> > | Relation between dimer & Ising models
# Julien Dubedat, | |||||||

## Related surveys
Stanislav Smirnov, | ||||||||

Deleted: | ||||||||

< < | # Julien Dubedat, Topics on abelian spin models and related problems. Probability Surveys 8, 374-402 (2011). Link | |||||||

Hugo Duminil-Copin and Stanislav Smirnov, Conformal invariance of lattice models. Lecture notes for the 2010 Clay Mathematical Institute Summer School. http://arxiv.org/abs/1109.1549
#Geoffrey Grimmett, |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 39 to 39 | ||||||||

| ||||||||

Changed: | ||||||||

< < |
| |||||||

> > |
| |||||||

| ||||||||

Added: | ||||||||

> > |
| |||||||

## Relevant papers covered (so far & soon) |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 33 to 33 | ||||||||

| ||||||||

Changed: | ||||||||

< < |
| |||||||

> > |
| |||||||

| ||||||||

Line: 60 to 60 | ||||||||

Dmitry Chelkak and Stanislav Smirnov, Discrete complex analysis on isoradial graphs. arXiv | ||||||||

Added: | ||||||||

> > | Time change, Dirichlet forms, and more potential theory
Z.-Q. Chen and Masatoshi Fukushima, | |||||||

Hausdorff dimension of planar Brownian motion
Gregory F. Lawler, Oded Schramm, and Wendelin Werner, |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 30 to 30 | ||||||||

| ||||||||

Changed: | ||||||||

< < |
| |||||||

> > |
| |||||||

| ||||||||

Line: 42 to 42 | ||||||||

| ||||||||

Deleted: | ||||||||

< < | ## Tentative syllabus (which is soon becoming outdated)
We will start with Kenyon's proof that the zero-mean height function associated with domino tilings of planar domains converges to the corresponding Gaussian free field. This will serve as nice review of concepts such as the Temperleyan tilings and Kasteleyn matrices ( | |||||||

## Relevant papers covered (so far & soon)
| ||||||||

Line: 54 to 50 | ||||||||

Richard Kenyon, Dominos and the Gaussian Free Field. Ann. Probab. 29, 1128-1137 (2001). Euclid | ||||||||

Added: | ||||||||

> > | Scott Sheffield, Gaussian free fields for mathematicians. Probability Theory & Related Fields 139, 521-541 (2007). arXiv | |||||||

Discrete complex analysis
Christian Mercat, | ||||||||

Line: 72 to 70 | ||||||||

Stanislav Smirnov, Discrete Complex Analysis and Probability. Proceedings of the International Congress of Mathematicians (ICM), Hyderabad, India (2010). ArXiv | ||||||||

Deleted: | ||||||||

< < | Scott Sheffield, Gaussian free fields for mathematicians. Probability Theory & Related Fields 139, 521-541 (2007). http://arxiv.org/abs/math/0312099 | |||||||

# Julien Dubedat, Topics on abelian spin models and related problems. Probability Surveys 8, 374-402 (2011). Link
Hugo Duminil-Copin and Stanislav Smirnov, |

Line: 1 to 1 | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | |||||||||||||

Line: 29 to 29 | |||||||||||||

| |||||||||||||

Changed: | |||||||||||||

< < |
| ||||||||||||

> > |
| ||||||||||||

| |||||||||||||

Changed: | |||||||||||||

< < |
| ||||||||||||

> > |
| ||||||||||||

## Tentative syllabus (which is soon becoming outdated) |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 6 to 6 | ||||||||

## Topic: Statistical mechanics on discrete graphs and its scaling limits | ||||||||

Changed: | ||||||||

< < | Fridays 3:00 - 4:30 (when BRB calls!), Malott 205.Time & space coordinates: | |||||||

> > | Fridays 2:30 - 4:30 (when BRB calls!), Malott 205.Time & space coordinates: | |||||||

Mark Cerenzia, Joe Chen, Baris Ugurcan, Tianyi ZhengRegular participants: |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 43 to 44 | ||||||||

## Tentative syllabus (which is soon becoming outdated) | ||||||||

Changed: | ||||||||

< < | We will start with Kenyon's proof (Papers 1 & 2) that the zero-mean height function associated with domino tilings of planar domains converges to the corresponding Gaussian free field. This will serve as nice review of concepts such as the Temperleyan tilings and Kasteleyn matrices ( combinatorics), (discrete) complex analysis, and random fields ( probability). The latter topics can be reinforced through Papers 3 & 4, pending interest. Then we move onto a general survey of abelian spin models (Paper 5), as a preparation for discussing connections between critical spin models, duality, and order-disorder variable pairing (e.g. parafermions, bosonization). | |||||||

> > | We will start with Kenyon's proof that the zero-mean height function associated with domino tilings of planar domains converges to the corresponding Gaussian free field. This will serve as nice review of concepts such as the Temperleyan tilings and Kasteleyn matrices ( combinatorics), (discrete) complex analysis, and random fields ( probability). The latter topics can be reinforced pending interest. Then we move onto a general survey of abelian spin models, as a preparation for discussing connections between critical spin models, duality, and order-disorder variable pairing (e.g. parafermions, bosonization).
## Relevant papers covered (so far & soon)
Richard Kenyon,
Richard Kenyon, | |||||||

Changed: | ||||||||

< < | ## Starters | |||||||

> > | Discrete complex analysis | |||||||

Changed: | ||||||||

< < | 1) Richard Kenyon, Conformal invariance of domino tiling. Ann. Probab. 28, 759-795 (2000). Euclid | |||||||

> > | Christian Mercat, Discrete Riemann Surfaces and the Ising Model. Comm. Math. Phys. 218, 177-216 (2001). SpringerLink arXiv | |||||||

Changed: | ||||||||

< < | 2) Richard Kenyon, Dominos and the Gaussian Free Field. Ann. Probab. 29, 1128-1137 (2001). Euclid | |||||||

> > | Richard Kenyon, The Laplacian and Dirac operators on critical planar graphs. Inventiones Mathematicae. 150, 409-439 (2002). SpringerLink arXiv | |||||||

Changed: | ||||||||

< < | 3) Stanislav Smirnov, Discrete Complex Analysis and Probability. Proceedings of the International Congress of Mathematicians (ICM), Hyderabad, India (2010). ArXiv | |||||||

> > | Dmitry Chelkak and Stanislav Smirnov, Discrete complex analysis on isoradial graphs. arXiv | |||||||

Changed: | ||||||||

< < | 4) Scott Sheffield, Gaussian free fields for mathematicians. Probability Theory & Related Fields 139, 521-541 (2007). http://arxiv.org/abs/math/0312099 | |||||||

> > | Hausdorff dimension of planar Brownian motion
Gregory F. Lawler, Oded Schramm, and Wendelin Werner, (see also references within) | |||||||

Deleted: | ||||||||

< < | 5)# Julien Dubedat, Topics on abelian spin models and related problems. Probability Surveys 8, 374-402 (2011). Link | |||||||

## Related surveys | ||||||||

Added: | ||||||||

> > | Stanislav Smirnov, Discrete Complex Analysis and Probability. Proceedings of the International Congress of Mathematicians (ICM), Hyderabad, India (2010). ArXiv
Scott Sheffield,
# Julien Dubedat, | |||||||

Hugo Duminil-Copin and Stanislav Smirnov, Conformal invariance of lattice models. Lecture notes for the 2010 Clay Mathematical Institute Summer School. http://arxiv.org/abs/1109.1549
#Geoffrey Grimmett, |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 27 to 27 | ||||||||

| ||||||||

Changed: | ||||||||

< < |
| |||||||

> > |
| |||||||

| ||||||||

Line: 39 to 39 | ||||||||

| ||||||||

Changed: | ||||||||

< < |
| |||||||

> > |
| |||||||

Changed: | ||||||||

< < | ## Tentative syllabus | |||||||

> > | ## Tentative syllabus (which is soon becoming outdated) | |||||||

We will start with Kenyon's proof (Papers 1 & 2) that the zero-mean height function associated with domino tilings of planar domains converges to the corresponding Gaussian free field. This will serve as nice review of concepts such as the Temperleyan tilings and Kasteleyn matrices ( combinatorics), (discrete) complex analysis, and random fields ( probability). The latter topics can be reinforced through Papers 3 & 4, pending interest. Then we move onto a general survey of abelian spin models (Paper 5), as a preparation for discussing connections between critical spin models, duality, and order-disorder variable pairing (e.g. parafermions, bosonization). |

Line: 1 to 1 | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | |||||||||||||||||||

Line: 19 to 19 | |||||||||||||||||||

For more information or expression of interest please contact Joe Chen (joe.p.chen@cornell.edu).
## Schedule | |||||||||||||||||||

Changed: | |||||||||||||||||||

< < | |||||||||||||||||||

> > | |||||||||||||||||||

| |||||||||||||||||||

Line: 27 to 27 | |||||||||||||||||||

| |||||||||||||||||||

Changed: | |||||||||||||||||||

< < |
| ||||||||||||||||||

> > |
| ||||||||||||||||||

| |||||||||||||||||||

Added: | |||||||||||||||||||

> > |
| ||||||||||||||||||

Deleted: | |||||||||||||||||||

< < | Further topics TBD: A session devoted to potential theory & harmonic measures may be in the offing. | ||||||||||||||||||

## Tentative syllabus
We will start with Kenyon's proof (Papers 1 & 2) that the zero-mean height function associated with domino tilings of planar domains converges to the corresponding Gaussian free field. This will serve as nice review of concepts such as the Temperleyan tilings and Kasteleyn matrices ( | |||||||||||||||||||

Line: 74 to 84 | |||||||||||||||||||

June 4-29: PIMS Probability Summer School, University of British Columbia, Vancouver, BC. Application is closed. | |||||||||||||||||||

Changed: | |||||||||||||||||||

< < | June 18-29: St. Petersburg Summer School in Probability & Statistical Physics, Chebyshev Laboratory, St. Petersburg, Russia. Application is closed. | ||||||||||||||||||

> > | June 18-29: St. Petersburg Summer School in Probability & Statistical Physics, Chebyshev Laboratory, St. Petersburg, Russia. Application is closed. | ||||||||||||||||||

July 8-21: 42nd Probability Summer School in St. Flour, St. Flour, France. Registration opens in February. |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 59 to 60 | ||||||||

## Templates for reading materials | ||||||||

Added: | ||||||||

> > | Gabor Pete's course "Critical phenomena and conformal invariance in the plane" at Budapest University of Technology and Economics: Spring 2012. | |||||||

MIT probability group reading seminar on 2D statistical physics: Fall 2010.
MIT Math 18.177: Topics in Stochastic processes, taught by Scott Sheffield. Fall 2009, Fall 2011. | ||||||||

Line: 71 to 74 | ||||||||

June 4-29: PIMS Probability Summer School, University of British Columbia, Vancouver, BC. Application is closed. | ||||||||

Changed: | ||||||||

< < | June 18-29: St. Petersburg Summer School in Probability & Statistical Physics, Chebyshev Laboratory, St. Petersburg, Russia. Deadline: Feb 12, 2012. | |||||||

> > | June 18-29: St. Petersburg Summer School in Probability & Statistical Physics, Chebyshev Laboratory, St. Petersburg, Russia. Application is closed. | |||||||

July 8-21: 42nd Probability Summer School in St. Flour, St. Flour, France. Registration opens in February. |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 25 to 25 | ||||||||

| ||||||||

Changed: | ||||||||

< < |
| |||||||

> > |
| |||||||

| ||||||||

Changed: | ||||||||

< < |
| |||||||

> > |
| |||||||

Further topics TBD: A session devoted to potential theory & harmonic measures may be in the offing. |

Line: 1 to 1 | |||||||||
---|---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | |||||||||

Line: 25 to 25 | |||||||||

| |||||||||

Changed: | |||||||||

< < |
| ||||||||

> > |
| ||||||||

Further topics TBD: A session devoted to potential theory & harmonic measures may be in the offing.
## Tentative syllabus |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 6 to 6 | ||||||||

## Topic: Statistical mechanics on discrete graphs and its scaling limits | ||||||||

Changed: | ||||||||

< < | Fridays 2:30 - 4:30 (when BRB calls!), Malott 205.Time & space coordinates: | |||||||

> > | Fridays 3:00 - 4:30 (when BRB calls!), Malott 205.Time & space coordinates: | |||||||

Mark Cerenzia, Joe Chen, Baris Ugurcan, Tianyi ZhengRegular participants: |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 28 to 28 | ||||||||

| ||||||||

Changed: | ||||||||

< < | Further topics TBA | |||||||

> > | Further topics TBD: A session devoted to potential theory & harmonic measures may be in the offing. | |||||||

## Tentative syllabus
We will start with Kenyon's proof (Papers 1 & 2) that the zero-mean height function associated with domino tilings of planar domains converges to the corresponding Gaussian free field. This will serve as nice review of concepts such as the Temperleyan tilings and Kasteleyn matrices ( |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 23 to 23 | ||||||||

| ||||||||

Changed: | ||||||||

< < |
| |||||||

> > |
| |||||||

| ||||||||

Added: | ||||||||

> > |
| |||||||

Further topics TBA
## Tentative syllabus |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 22 to 22 | ||||||||

| ||||||||

Changed: | ||||||||

< < |
| |||||||

> > |
| |||||||

| ||||||||

Changed: | ||||||||

< < |
| |||||||

> > |
| |||||||

Further topics TBA
## Tentative syllabus |

Line: 1 to 1 | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||||||||||

Line: 19 to 19 | ||||||||||||||||

For more information or expression of interest please contact Joe Chen (joe.p.chen@cornell.edu).
## Schedule | ||||||||||||||||

Changed: | ||||||||||||||||

< < |
| |||||||||||||||

> > |
| |||||||||||||||

Further topics TBA
## Tentative syllabus |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 14 to 14 | ||||||||

The goals of this seminar are to understand these discrete models and their limiting objects, and equally important, to learn the techniques used to prove convergence to the scaling limit. As such the emphasis will be on reading the mathematical proofs, as opposed to learning about heuristics. (Though it is often possible to understand the heuristic idea behind a rigorous result...) | ||||||||

Changed: | ||||||||

< < | Not afraid of measure-theoretic probability theory (as covered in MATH 6710-6720) and complex analysis (MATH 6120). No prior experience with statistical mechanics is needed. Prerequisites: | |||||||

> > | Not afraid of measure-theoretic probability theory (as covered in MATH 6710-6720) and complex analysis (MATH 6120). No prior experience with statistical mechanics is needed. The evolving choice of topics will follow the philosophy (in the words of L. Gross): Prerequisites: From each according to her/his taste. To each according to his/her interest. | |||||||

For more information or expression of interest please contact Joe Chen (joe.p.chen@cornell.edu).
## Schedule | ||||||||

Line: 25 to 25 | ||||||||

Further topics TBA | ||||||||

Changed: | ||||||||

< < | ## Tentative syllabus (as of 01/23/12) | |||||||

> > | ## Tentative syllabus
We will start with Kenyon's proof (Papers 1 & 2) that the zero-mean height function associated with domino tilings of planar domains converges to the corresponding Gaussian free field. This will serve as nice review of concepts such as the Temperleyan tilings and Kasteleyn matrices ( | |||||||

Deleted: | ||||||||

< < | We will start with Kenyon's proof (Papers 1 & 2) that the zero-mean height function associated with domino tilings of planar domains converges to the corresponding Gaussian free field. This will serve as nice review of concepts such as the Temperleyan tilings ( combinatorics), (discrete) complex analysis, and random fields ( probability). The latter topics can be reinforced through Papers 3 & 4, pending interest. Then we move onto a general survey of abelian spin models (Paper 5), as a preparation for learning about connections between critical spin models and discrete complex analysis (e.g. parafermions). | |||||||

## Starters
1) Richard Kenyon, |

Line: 1 to 1 | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | |||||||||||||

Line: 19 to 19 | |||||||||||||

For more information or expression of interest please contact Joe Chen (joe.p.chen@cornell.edu).
## Schedule | |||||||||||||

Changed: | |||||||||||||

< < | 2/2 (Fri): Conformal invariance of domino tiling, Part I (Joe Chen)
2/9 (Fri): Conformal invariance of domino tiling, Part II 2/16 (Fri): Dominos and the Gaussian Free Field | ||||||||||||

> > |
| ||||||||||||

Further topics TBA
## Tentative syllabus (as of 01/23/12) |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 6 to 6 | ||||||||

## Topic: Statistical mechanics on discrete graphs and its scaling limits | ||||||||

Changed: | ||||||||

< < | Fridays 2:30 - 4:30 (when BRB calls!), Malott 205.Tentative time & place: | |||||||

> > | Fridays 2:30 - 4:30 (when BRB calls!), Malott 205.Time & space coordinates: | |||||||

Changed: | ||||||||

< < | Mark Cerenzia, Joe Chen, Baris Ugurcan, Tianyi ZhengRegular participants: | |||||||

> > | Mark Cerenzia, Joe Chen, Baris Ugurcan, Tianyi ZhengRegular participants: | |||||||

This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. The focus will be on statistical mechanics models on discrete lattices or isoradial graphs in two dimensions, which include percolation, Ising/Potts spin models, height function associated with domino tilings, and random quadrangulations of surfaces. We wish to understand their behavior in the scaling limit, that is, when either the size of the graph tends to infinity, or the underlying mesh radius goes to zero. Remarkably, many of these models "at criticality" converge to conformally invariant objects such as Schramm-Loewner evolution (SLE) curves, Gaussian free fields, or quantum gravity models.Description: |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 8 to 8 | ||||||||

Fridays 2:30 - 4:30 (when BRB calls!), Malott 205.Tentative time & place: | ||||||||

Changed: | ||||||||

< < | Joe Chen, Baris Ugurcan, Tianyi ZhengRegular participants: | |||||||

> > | Mark Cerenzia, Joe Chen, Baris Ugurcan, Tianyi ZhengRegular participants: | |||||||

This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. The focus will be on statistical mechanics models on discrete lattices or isoradial graphs in two dimensions, which include percolation, Ising/Potts spin models, height function associated with domino tilings, and random quadrangulations of surfaces. We wish to understand their behavior in the scaling limit, that is, when either the size of the graph tends to infinity, or the underlying mesh radius goes to zero. Remarkably, many of these models "at criticality" converge to conformally invariant objects such as Schramm-Loewner evolution (SLE) curves, Gaussian free fields, or quantum gravity models.Description: |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 6 to 6 | ||||||||

## Topic: Statistical mechanics on discrete graphs and its scaling limits | ||||||||

Changed: | ||||||||

< < | Fridays 2:30 - 4:30 (when BRB calls!), room to be confirmed.Tentative time & place: | |||||||

> > | Fridays 2:30 - 4:30 (when BRB calls!), Malott 205.
Tentative time & place:
| |||||||

This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. The focus will be on statistical mechanics models on discrete lattices or isoradial graphs in two dimensions, which include percolation, Ising/Potts spin models, height function associated with domino tilings, and random quadrangulations of surfaces. We wish to understand their behavior in the scaling limit, that is, when either the size of the graph tends to infinity, or the underlying mesh radius goes to zero. Remarkably, many of these models "at criticality" converge to conformally invariant objects such as Schramm-Loewner evolution (SLE) curves, Gaussian free fields, or quantum gravity models.Description: | ||||||||

Line: 14 to 16 | ||||||||

Not afraid of measure-theoretic probability theory (as covered in MATH 6710-6720) and complex analysis (MATH 6120). No prior experience with statistical mechanics is needed. Prerequisites: | ||||||||

Changed: | ||||||||

< < | For more information or expression of interest please contact Joe P. Chen (joe.p.chen@cornell.edu). | |||||||

> > | For more information or expression of interest please contact Joe Chen (joe.p.chen@cornell.edu). | |||||||

## Schedule2/2 (Fri): Conformal invariance of domino tiling, Part I (Joe Chen) |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 6 to 6 | ||||||||

## Topic: Statistical mechanics on discrete graphs and its scaling limits | ||||||||

Changed: | ||||||||

< < | Fridays 2:30 - 4:30 (when BRB calls!), room to be confirmed.Time & place: | |||||||

> > | Fridays 2:30 - 4:30 (when BRB calls!), room to be confirmed.Tentative time & place: | |||||||

This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. The focus will be on statistical mechanics models on discrete lattices or isoradial graphs in two dimensions, which include percolation, Ising/Potts spin models, height function associated with domino tilings, and random quadrangulations of surfaces. We wish to understand their behavior in the scaling limit, that is, when either the size of the graph tends to infinity, or the underlying mesh radius goes to zero. Remarkably, many of these models "at criticality" converge to conformally invariant objects such as Schramm-Loewner evolution (SLE) curves, Gaussian free fields, or quantum gravity models.Description: |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 6 to 6 | ||||||||

## Topic: Statistical mechanics on discrete graphs and its scaling limits | ||||||||

Changed: | ||||||||

< < | TBD after class schedules have settled down during the first week.Time & place: | |||||||

> > | Fridays 2:30 - 4:30 (when BRB calls!), room to be confirmed.Time & place: | |||||||

This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. The focus will be on statistical mechanics models on discrete lattices or isoradial graphs in two dimensions, which include percolation, Ising/Potts spin models, height function associated with domino tilings, and random quadrangulations of surfaces. We wish to understand their behavior in the scaling limit, that is, when either the size of the graph tends to infinity, or the underlying mesh radius goes to zero. Remarkably, many of these models "at criticality" converge to conformally invariant objects such as Schramm-Loewner evolution (SLE) curves, Gaussian free fields, or quantum gravity models.Description: | ||||||||

Line: 15 to 15 | ||||||||

Not afraid of measure-theoretic probability theory (as covered in MATH 6710-6720) and complex analysis (MATH 6120). No prior experience with statistical mechanics is needed.
Prerequisites: For more information or expression of interest please contact Joe P. Chen (joe.p.chen@cornell.edu). | ||||||||

Added: | ||||||||

> > | ## Schedule2/2 (Fri): Conformal invariance of domino tiling, Part I (Joe Chen) 2/9 (Fri): Conformal invariance of domino tiling, Part II 2/16 (Fri): Dominos and the Gaussian Free Field Further topics TBA | |||||||

## Tentative syllabus (as of 01/23/12)
We will start with Kenyon's proof (Papers 1 & 2) that the zero-mean height function associated with domino tilings of planar domains converges to the corresponding Gaussian free field. This will serve as nice review of concepts such as the Temperleyan tilings ( |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 28 to 28 | ||||||||

4) Scott Sheffield, Gaussian free fields for mathematicians. Probability Theory & Related Fields 139, 521-541 (2007). http://arxiv.org/abs/math/0312099 | ||||||||

Changed: | ||||||||

< < | 5)* Julien Dubedat, Topics on abelian spin models and related problems. Probability Surveys 8, 374-402 (2011). Link | |||||||

> > | 5)# Julien Dubedat, Topics on abelian spin models and related problems. Probability Surveys 8, 374-402 (2011). Link | |||||||

## Related surveys
Hugo Duminil-Copin and Stanislav Smirnov, | ||||||||

Changed: | ||||||||

< < | *Geoffrey Grimmett, Three theorems in discrete random geometry. To be published in Probability Surveys (2011+). http://arxiv.org/abs/1110.2395 | |||||||

> > | #Geoffrey Grimmett, Three theorems in discrete random geometry. Probability Surveys 8, 403-441 (2011). Link | |||||||

Richard Kenyon, Lectures on dimers. In Statistical Mechanics, IAS/Park City Mathematical Series 2007, S. Sheffield & T. Spencer, eds. (2009). (pdf)
Nike Sun, | ||||||||

Changed: | ||||||||

< < | [* indicate expanded lecture notes from the 2011 Cornell Probability Summer School.] | |||||||

> > | [# indicate expanded lecture notes from the 2011 Cornell Probability Summer School.] | |||||||

## Templates for reading materials | ||||||||

Line: 52 to 52 | ||||||||

## Info on 2012 summer schools | ||||||||

Changed: | ||||||||

< < | June 4-29: PIMS Probability Summer School, University of British Columbia, Vancouver, BC. Deadline: Dec 30, 2011. | |||||||

> > | June 4-29: PIMS Probability Summer School, University of British Columbia, Vancouver, BC. Application is closed. | |||||||

June 18-29: St. Petersburg Summer School in Probability & Statistical Physics, Chebyshev Laboratory, St. Petersburg, Russia. Deadline: Feb 12, 2012. | ||||||||

Added: | ||||||||

> > | July 8-21: 42nd Probability Summer School in St. Flour, St. Flour, France. Registration opens in February. | |||||||

July 16-27: Cornell Probability Summer School. |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 6 to 6 | ||||||||

## Topic: Statistical mechanics on discrete graphs and its scaling limits | ||||||||

Changed: | ||||||||

< < | TBA. Please fill out this scheduling form to help us set a time.Time & place: | |||||||

> > | TBD after class schedules have settled down during the first week.Time & place: | |||||||

Changed: | ||||||||

< < | This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. The focus will be on statistical mechanics models on discrete lattices or isoradial graphs in two dimensions, which include percolation, Ising/Potts spin models, height function associated with domino tilings, and quantum gravity models. We wish to understand their behavior in the scaling limit, that is, when either the size of the graph tends to infinity, or the underlying mesh radius goes to zero. Remarkably, many of these models at criticality converge to conformally invariant objects such as Schramm-Loewner evolution (SLE) curves or Gaussian free fields.Description (as of Dec 2011): | |||||||

> > | This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. The focus will be on statistical mechanics models on discrete lattices or isoradial graphs in two dimensions, which include percolation, Ising/Potts spin models, height function associated with domino tilings, and random quadrangulations of surfaces. We wish to understand their behavior in the scaling limit, that is, when either the size of the graph tends to infinity, or the underlying mesh radius goes to zero. Remarkably, many of these models "at criticality" converge to conformally invariant objects such as Schramm-Loewner evolution (SLE) curves, Gaussian free fields, or quantum gravity models.Description: | |||||||

The goals of this seminar are to understand these discrete models and their limiting objects, and equally important, to learn the techniques used to prove convergence to the scaling limit. As such the emphasis will be on reading the mathematical proofs, as opposed to learning about heuristics. (Though it is often possible to understand the heuristic idea behind a rigorous result...) | ||||||||

Deleted: | ||||||||

< < | Tentatively we plan to meet once a week for 60-90 minutes. The exact scope of topics covered will be announced prior to the spring semester, and may evolve according to the interests of the participants. | |||||||

Not afraid of measure-theoretic probability theory (as covered in MATH 6710-6720) and complex analysis (MATH 6120). No prior experience with statistical mechanics is needed.
Prerequisites: For more information or expression of interest please contact Joe P. Chen (joe.p.chen@cornell.edu). | ||||||||

Added: | ||||||||

> > | ## Tentative syllabus (as of 01/23/12) | |||||||

Changed: | ||||||||

< < | ## Prime surveys | |||||||

> > | We will start with Kenyon's proof (Papers 1 & 2) that the zero-mean height function associated with domino tilings of planar domains converges to the corresponding Gaussian free field. This will serve as nice review of concepts such as the Temperleyan tilings ( combinatorics), (discrete) complex analysis, and random fields ( probability). The latter topics can be reinforced through Papers 3 & 4, pending interest. Then we move onto a general survey of abelian spin models (Paper 5), as a preparation for learning about connections between critical spin models and discrete complex analysis (e.g. parafermions).
## Starters | |||||||

Changed: | ||||||||

< < | Hugo Duminil-Copin and Stanislav Smirnov, Conformal invariance of lattice models. Lecture notes for the 2010 Clay Mathematical Institute Summer School. http://arxiv.org/abs/1109.1549 | |||||||

> > | 1) Richard Kenyon, Conformal invariance of domino tiling. Ann. Probab. 28, 759-795 (2000). Euclid | |||||||

Changed: | ||||||||

< < | Geoffrey Grimmett, Three theorems in discrete random geometry. To be published in Probability Surveys (2011+). http://arxiv.org/abs/1110.2395 | |||||||

> > | 2) Richard Kenyon, Dominos and the Gaussian Free Field. Ann. Probab. 29, 1128-1137 (2001). Euclid | |||||||

Changed: | ||||||||

< < | Richard Kenyon, Lectures on dimers. In Statistical Mechanics, IAS/Park City Mathematical Series 2007, S. Sheffield & T. Spencer, eds. (2009). (pdf) | |||||||

> > | 3) Stanislav Smirnov, Discrete Complex Analysis and Probability. Proceedings of the International Congress of Mathematicians (ICM), Hyderabad, India (2010). ArXiv
4) Scott Sheffield, | |||||||

Changed: | ||||||||

< < | Scott Sheffield, Gaussian free fields for mathematicians. Probability Theory & Related Fields 139, 521-541 (2007). http://arxiv.org/abs/math/0312099 | |||||||

> > | 5)* Julien Dubedat, Topics on abelian spin models and related problems. Probability Surveys 8, 374-402 (2011). Link
## Related surveys | |||||||

Changed: | ||||||||

< < | Stanislav Smirnov, Discrete Complex Analysis and Probability. Proceedings of the International Congress of Mathematicians (ICM), Hyderabad, India (2010). http://arxiv.org/abs/1009.6077 | |||||||

> > | Hugo Duminil-Copin and Stanislav Smirnov, Conformal invariance of lattice models. Lecture notes for the 2010 Clay Mathematical Institute Summer School. http://arxiv.org/abs/1109.1549
*Geoffrey Grimmett,
Richard Kenyon, | |||||||

Nike Sun, Conformally invariant scaling limits in planar critical percolation. Probability Surveys , 155-209 (2011). (pdf download)8 | ||||||||

Added: | ||||||||

> > | [* indicate expanded lecture notes from the 2011 Cornell Probability Summer School.] | |||||||

## Templates for reading materials |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 10 to 10 | ||||||||

This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. The focus will be on statistical mechanics models on discrete lattices or isoradial graphs in two dimensions, which include percolation, Ising/Potts spin models, height function associated with domino tilings, and quantum gravity models. We wish to understand their behavior in the scaling limit, that is, when either the size of the graph tends to infinity, or the underlying mesh radius goes to zero. Remarkably, many of these models at criticality converge to conformally invariant objects such as Schramm-Loewner evolution (SLE) curves or Gaussian free fields.Description (as of Dec 2011): | ||||||||

Changed: | ||||||||

< < | The goals of this seminar are to understand these discrete models and their limiting objects, and along the way learn the techniques used to prove convergence to the scaling limit. | |||||||

> > | The goals of this seminar are to understand these discrete models and their limiting objects, and equally important, to learn the techniques used to prove convergence to the scaling limit. As such the emphasis will be on reading the mathematical proofs, as opposed to learning about heuristics. (Though it is often possible to understand the heuristic idea behind a rigorous result...) | |||||||

Tentatively we plan to meet once a week for 60-90 minutes. The exact scope of topics covered will be announced prior to the spring semester, and may evolve according to the interests of the participants. |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 16 to 16 | ||||||||

Not afraid of measure-theoretic probability theory (as covered in MATH 6710-6720) and complex analysis (MATH 6120). No prior experience with statistical mechanics is needed. Prerequisites: | ||||||||

Changed: | ||||||||

< < | For more information and expression of interest please contact Joe P. Chen (joe.p.chen@cornell.edu). | |||||||

> > | For more information or expression of interest please contact Joe P. Chen (joe.p.chen@cornell.edu). | |||||||

## Prime surveys | ||||||||

Line: 32 to 32 | ||||||||

Nike Sun, Conformally invariant scaling limits in planar critical percolation. Probability Surveys , 155-209 (2011). (pdf download)8 | ||||||||

Changed: | ||||||||

< < | ## Relevant links | |||||||

> > | ## Templates for reading materials | |||||||

MIT probability group reading seminar on 2D statistical physics: Fall 2010. | ||||||||

Line: 40 to 40 | ||||||||

Informal seminar on SLE at UC Berkeley, year unknown. | ||||||||

Changed: | ||||||||

< < | A collection of literatures by Pierre Nolin is here. | |||||||

> > | A collection of literatures by Pierre Nolin, both surveys and original papers, is here. | |||||||

## Info on 2012 summer schools |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 8 to 8 | ||||||||

TBA. Please fill out this scheduling form to help us set a time.Time & place: | ||||||||

Changed: | ||||||||

< < | This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. Geoff Grimmett's lecture notes would be a nice starting point, supplemented by the relevant literatures, such as his books on percolation & random cluster model, as well as recent works of Kenyon, Sheffield, Smirnov, etc.Description (as of Dec 2011): | |||||||

> > | This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. The focus will be on statistical mechanics models on discrete lattices or isoradial graphs in two dimensions, which include percolation, Ising/Potts spin models, height function associated with domino tilings, and quantum gravity models. We wish to understand their behavior in the scaling limit, that is, when either the size of the graph tends to infinity, or the underlying mesh radius goes to zero. Remarkably, many of these models at criticality converge to conformally invariant objects such as Schramm-Loewner evolution (SLE) curves or Gaussian free fields.Description (as of Dec 2011): | |||||||

Changed: | ||||||||

< < | We could also concentrate on models in two dimensions, where many discrete models at criticality are believed (by physicists) and now proved (by mathematicians) to enjoy conformal invariance. These include percolation, spin models, height function associated with domino tilings, and quantum gravity models. The limiting objects often turn out to be instances of Schramm-Loewner evolution (SLE) or Gaussian free field. | |||||||

> > | The goals of this seminar are to understand these discrete models and their limiting objects, and along the way learn the techniques used to prove convergence to the scaling limit. | |||||||

Changed: | ||||||||

< < | An important goal is to learn the techniques used to prove these hard and physically interesting results.
Tentatively we plan to meet once a week for 60-90 minutes. The exact scope of topics covered will be announced before the spring semester starts, and may evolve according to the interests of the participants. | |||||||

> > | Tentatively we plan to meet once a week for 60-90 minutes. The exact scope of topics covered will be announced prior to the spring semester, and may evolve according to the interests of the participants. | |||||||

Not afraid of measure-theoretic probability theory (as covered in MATH 6710-6720) and complex analysis (MATH 6120). No prior experience with statistical mechanics is needed. Prerequisites: |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

## Probability Reading Group, Spring 2012 | ||||||||

Line: 6 to 6 | ||||||||

## Topic: Statistical mechanics on discrete graphs and its scaling limits | ||||||||

Changed: | ||||||||

< < | TBATime & place: | |||||||

> > | TBA. Please fill out this scheduling form to help us set a time.Time & place: | |||||||

Changed: | ||||||||

< < | This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. Geoff Grimmett's lecture notes (http://arxiv.org/abs/1110.2395) would be a nice starting point, supplemented by the relevant literatures, such as his books on percolation & random cluster model, as well as recent works of Kenyon, Sheffield, Smirnov, etc.Description (as of Dec 2011): | |||||||

> > | This informal reading group will be in some sense a continuation and/or elaboration of the materials given in the 2011 Cornell Probability Summer School. Geoff Grimmett's lecture notes would be a nice starting point, supplemented by the relevant literatures, such as his books on percolation & random cluster model, as well as recent works of Kenyon, Sheffield, Smirnov, etc.Description (as of Dec 2011): | |||||||

Changed: | ||||||||

< < | We could also concentrate on models in two dimensions, where many discrete models at criticality are believed (by physicists) and now proved (by mathematicians) to enjoy conformal invariance. These include percolation, spin models, height function associated with domino tilings, and quantum gravity models. The limiting objects often turn out to be instances of SLE, Gaussian free field, etc. | |||||||

> > | We could also concentrate on models in two dimensions, where many discrete models at criticality are believed (by physicists) and now proved (by mathematicians) to enjoy conformal invariance. These include percolation, spin models, height function associated with domino tilings, and quantum gravity models. The limiting objects often turn out to be instances of Schramm-Loewner evolution (SLE) or Gaussian free field. | |||||||

An important goal is to learn the techniques used to prove these hard and physically interesting results. | ||||||||

Line: 26 to 26 | ||||||||

Geoffrey Grimmett, Three theorems in discrete random geometry. To be published in Probability Surveys (2011+). http://arxiv.org/abs/1110.2395 | ||||||||

Changed: | ||||||||

< < | Richard Kenyon, Lectures on dimers. In Statistical Mechanics, IAS/Park City Mathematical Series 2007, eds. S. Sheffield & T. Spencer (2009). http://www.math.brown.edu/~rkenyon/papers/dimerlecturenotes.pdf | |||||||

> > | Richard Kenyon, Lectures on dimers. In Statistical Mechanics, IAS/Park City Mathematical Series 2007, S. Sheffield & T. Spencer, eds. (2009). (pdf) | |||||||

Changed: | ||||||||

< < | Scott Sheffield. Gaussian free fields for mathematicians. Probability Theory & Related Fields 139, 521-541 (2007). http://arxiv.org/abs/math/0312099 | |||||||

> > | Scott Sheffield, Gaussian free fields for mathematicians. Probability Theory & Related Fields 139, 521-541 (2007). http://arxiv.org/abs/math/0312099 | |||||||

Changed: | ||||||||

< < | Stanislav Smirnov. Discrete Complex Analysis and Probability. Proceedings of the International Congress of Mathematicians (ICM), Hyderabad, India (2010). http://arxiv.org/abs/1009.6077 | |||||||

> > | Stanislav Smirnov, Discrete Complex Analysis and Probability. Proceedings of the International Congress of Mathematicians (ICM), Hyderabad, India (2010). http://arxiv.org/abs/1009.6077 | |||||||

Changed: | ||||||||

< < | Nike Sun, Conformally invariant scaling limits in planar critical percolation. Probability Surveys , 155-209 (2011). http://www.i-journals.org/ps/include/getdoc.php?id=726&article=180&mode=pdf8 | |||||||

> > | Nike Sun, Conformally invariant scaling limits in planar critical percolation. Probability Surveys , 155-209 (2011). (pdf download)8 | |||||||

## Relevant links | ||||||||

Changed: | ||||||||

< < | MIT probability group reading seminar on 2D statistical physics (Fall 2010): http://math.mit.edu/~asafnach/2dstatphysics.html. | |||||||

> > | MIT probability group reading seminar on 2D statistical physics: Fall 2010. | |||||||

Changed: | ||||||||

< < | Informal seminar on SLE at UC Berkeley (year unknown): http://www.eve.ucdavis.edu/plralph/sle-seminar/. | |||||||

> > | MIT Math 18.177: Topics in Stochastic processes, taught by Scott Sheffield. Fall 2009, Fall 2011. | |||||||

Changed: | ||||||||

< < | A collection of literatures by Pierre Nolin: http://cims.nyu.edu/~nolin/AdvancedTopics/References.pdf. | |||||||

> > | Informal seminar on SLE at UC Berkeley, year unknown.
A collection of literatures by Pierre Nolin is here. | |||||||

## Info on 2012 summer schools | ||||||||

Changed: | ||||||||

< < | June 4-29: PIMS Probability Summer School, University of British Columbia, Vancouver, BC. Deadline: Dec 30, 2011. http://www.math.ubc.ca/Links/ssprob12/ | |||||||

> > | June 4-29: PIMS Probability Summer School, University of British Columbia, Vancouver, BC. Deadline: Dec 30, 2011. | |||||||

Changed: | ||||||||

< < | June 18-29: St. Petersburg Summer School in Probability & Statistical Physics, Chebyshev Laboratory, St. Petersburg, Russia. Deadline: Feb 12, 2012. http://spspsp.chebyshev.spb.ru/ | |||||||

> > | June 18-29: St. Petersburg Summer School in Probability & Statistical Physics, Chebyshev Laboratory, St. Petersburg, Russia. Deadline: Feb 12, 2012. | |||||||

Changed: | ||||||||

< < | July 16-27: Cornell Probability Summer School. http://www.math.duke.edu/~rtd/CPSS2012/index.html | |||||||

> > | July 16-27: Cornell Probability Summer School. |

Line: 1 to 1 | ||||||||
---|---|---|---|---|---|---|---|---|

Added: | ||||||||

> > |
## Probability Reading Group, Spring 2012
## Topic: Statistical mechanics on discrete graphs and its scaling limits
We could also concentrate on models in two dimensions, where many discrete models at criticality are believed (by physicists) and now proved (by mathematicians) to enjoy conformal invariance. These include percolation, spin models, height function associated with domino tilings, and quantum gravity models. The limiting objects often turn out to be instances of SLE, Gaussian free field, etc. An important goal is to learn the techniques used to prove these hard and physically interesting results. Tentatively we plan to meet once a week for 60-90 minutes. The exact scope of topics covered will be announced before the spring semester starts, and may evolve according to the interests of the participants.
For more information and expression of interest please contact Joe P. Chen (joe.p.chen@cornell.edu).
## Prime surveys
Hugo Duminil-Copin and Stanislav Smirnov,
Geoffrey Grimmett,
Richard Kenyon,
Scott Sheffield.
Stanislav Smirnov.
Nike Sun,
## Relevant linksMIT probability group reading seminar on 2D statistical physics (Fall 2010): http://math.mit.edu/~asafnach/2dstatphysics.html. Informal seminar on SLE at UC Berkeley (year unknown): http://www.eve.ucdavis.edu/plralph/sle-seminar/. A collection of literatures by Pierre Nolin: http://cims.nyu.edu/~nolin/AdvancedTopics/References.pdf.
## Info on 2012 summer schools
June 4-29: PIMS Probability Summer School, University of British Columbia, Vancouver, BC.
June 18-29: St. Petersburg Summer School in Probability & Statistical Physics, Chebyshev Laboratory, St. Petersburg, Russia. July 16-27: Cornell Probability Summer School. http://www.math.duke.edu/~rtd/CPSS2012/index.html |

View topic | History: r35 < r34 < r33 < r32 | More topic actions...