Difference: ProbabilityReadingGroup (28 vs. 29)

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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.
3/2 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.
 
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

 
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