Random walks on co-compact fuchsian groups

Random Walks on Co-compact Fuchsian Groups

It is proved that the Green’s function of a symmetric finite range randomwalk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R. It is also shown that Ancona’s inequalities extend to R, and therefore that the Martin boundary for R−potentials coincides with the natural geometric boundary S, and that the Martin kernel is uniformly Hölder continuous. Fi...

Random Walks in Compact Groups

Let X1, X2, . . . be independent identically distributed random elements of a compact group G. We discuss the speed of convergence of the law of the product Xl · · ·X1 to the Haar measure. We give poly-log estimates for certain finite groups and for compact semi-simple Lie groups. We improve earlier results of Solovay, Kitaev, Gamburd, Shahshahani and Dinai. 2010 Mathematics Subject Classificat...

Compact Deformations of Fuchsian Groups

Isoperimetric Profile and Random Walks on Locally Compact Solvable Groups

We study the large-scale geometry of a large class of amenable locally compact groups comprising all solvable algebraic groups over a local field and their discrete subgroups. We show that the isoperimetric profile of these groups is in some sense optimal among amenable groups. We use this fact to compute the probability of return of symmetric random walks, and to derive various other geometric...

Character Theory of Symmetric Groups, Subgroup Growth of Fuchsian Groups, and Random Walks