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| BRIGITTA VERMESI Mathematics Department University of Rochester Title: /Critical exponents for Brownian motion and random walk/ Abstract: In the past decade, there have been significant advances in the study of two-dimensional critical systems in statistical physics, in particular due to the introduction of Schramm Loewner Evolution (SLE). For example, some critical exponents for planar Brownian motion have been computed exactly using SLE. But what can we say about the same exponents in the case of 3-dimensional Brownian motion? To answer this question, we start by studying a somewhat simpler, but related problem: critical exponents for random walks on d-dimensional cylinders. In this talk, I will describe the random walk problem and explain how it relates to the 3-dimensional Brownian motion case. This leads to a conjecture about exponents for Brownian motion. |