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Probability Reading Group, Spring 2012 |
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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. |
| 4/13 |
SLE & planar Brownian motion, Part I |
Mark Cerenzia |
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| Introducing Mandelbrot's hypothesis and setup. |
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| Introducing Mandelbrot's conjecture that the Hausdorff dim of planar Brownian motion is 4/3, and setup. |
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| 4/20 |
Cover times, blanket times, and majorizing measures |
Tianyi Zheng |
| Based on Ding-Lee-Peres. |
| 4/27 |
SLE & planar Brownian motion, Part II |
Mark Cerenzia |
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| Discusses the SLE machinery which enables the proof of Mandelbrot's hypothesis. |
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| Discusses the SLE machinery which enables the proof of Mandelbrot's conjecture. |
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Relevant papers covered (so far & soon) |
