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Probability Reading Group, Spring 2012 |
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| Clarified the connection between the coupling function and the Green's function, and showed how $F_0, F_1$ enter into the moment formula of the height variation. We didn't have time to prove convergence to GFF, but all the necessary technical lemmas have been covered, so please read on your own. |
| 2/24 |
Discrete complex analysis on isoradial graphs |
Baris Ugurcan |
| Covered notions of harmonicity and holomorphicity on isoradial graphs; discrete exponential function; and mode of convergence of discrete harmonic functions to a true harmonic function in the continuum. |
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| 3/2 |
No meeting |
| Prospie visit day |
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| 3/9 |
Time change, trace Dirichlet forms, and relation to elementary potential theory |
Tianyi Zheng |
| Defined time changed process induced by additive functionals and Revuz measures. Covered local times, inverse local times, classical 2nd Ray-Knight theorem, construction of Dirichlet form for time-changed process. Example: RBM on a simply connected planar domain as a time change of RBM on the unit disc under conformal transformation. Mostly drawn from Chapter 5 of Chen-Fukushima. |
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| 3/16 |
No meeting |
| Day before spring break |
| 3/23 |
No meeting |
| Actual spring break |
| 3/30 |
SLE & planar Brownian motion, Part I |
Mark Cerenzia |
| See Lawler-Schramm-Werner. Some stochastic calculus will be covered. |
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| 4/6 |
(Tentative) Dimer observables, parafermions, and Ising correlators |
Joe Chen |
| aka "What I learned at MSRI while on extended spring break." |
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| 4/13 |
SLE & planar Brownian motion, Part II |
Mark Cerenzia |
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| 4/13 |
SLE & planar Brownian motion |
Mark Cerenzia |
| See Lawler-Schramm-Werner. Some stochastic calculus will be covered. |
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Relevant papers covered (so far & soon) |
