Ryokichi Tanaka

For every non-elementary hyperbolic group, we consider the Manhattan curve, which was originally introduced by M. Burger (1993), associated to any pair of (say) word metrics. It is convex; we show that it is continuously differentiable and moreover...

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...