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name="WebHome" |
Probability Reading Group, Spring 2012 |
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| 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. |
| 3/2 |
No meeting |
| Prospie visit day |
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| 3/9 |
Topics in potential theory |
Tianyi Zheng |
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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 |
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Dmitry Chelkak and Stanislav Smirnov, Discrete complex analysis on isoradial graphs. arXiv |
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> | Time change, Dirichlet forms, and more potential theory
Z.-Q. Chen and Masatoshi Fukushima, Symmetric Markov Processes, Time Changes, and Boundary Theory. Princeton University Press (2011). |
| | Hausdorff dimension of planar Brownian motion
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 |
