Probability Seminar: Ryokichi Tanaka

  • Date: 09/21/2016
  • Time: 15:00
Ryokichi Tanaka, University of Washington and Tohoku University

University of British Columbia


Dimension of harmonic measures in hyperbolic spaces


We discuss random walks on groups acting on hyperbolic spaces (e.g. the Poincaré disk), and their limiting behaviour 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.

Other Information: 

Location: ESB 2012