Time: Monday, May 23, 2016 at 2:30 pm.
Location: Smith Hall 102
Speaker: Ryokichi Tanaka (Tohoku University, Japan)
Title: Dimension of harmonic measures in hyperbolic spaces
Abstract: We discuss random walks on groups acting on hyperbolic spaces (e.g. the Poincare disk), and their limiting behavior on the boundary. The limiting distribution of the random walk (the harmonic measure) is of particular interest for description of bounded harmonic functions on the group (the Poisson boundary). We consider the Hausdorff dimension of harmonic measure on the boundary and give a formula in terms of the entropy and the drift under a general moment condition. Related recent results are also discussed during the talk.
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