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| META TOPICPARENT |
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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. |
| 3/9 |
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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| 4/6 |
(Tentative) Dimer observables, parafermions, and Ising correlators |
Joe Chen |
| aka "What I learned at MSRI while on extended spring break." |
| 4/13 |
SLE & planar Brownian motion |
Mark Cerenzia |
| See Lawler-Schramm-Werner. Some stochastic calculus will be covered. |
| TBA |
Cover times, blanket times, and majorizing measures |
Tianyi Zheng |
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| 4/13 |
SLE & planar Brownian motion, Part I |
Mark Cerenzia |
| Introducing Mandelbrot's hypothesis and setup. |
| 4/20 |
Cover times, blanket times, and majorizing measures |
Tianyi Zheng |
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| 4/27 |
SLE & planar Brownian motion, Part II |
Mark Cerenzia |
| Discusses the SLE machinery which enables the proof of Mandelbrot's hypothesis. |
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Relevant papers covered (so far & soon) |
