Difference: ProbabilityReadingGroup (34 vs. 35)

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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.
 
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.
 

Relevant papers covered (so far & soon)

 
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