Difference: ProbabilityReadingGroup (33 vs. 34)

Revision 342012-04-12 - jpc64

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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
 
Based on Ding-Lee-Peres.
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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.
 

Relevant papers covered (so far & soon)

 
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