Martin boundary covers Floyd boundary
Group Theory
2017-12-07 v3 Dynamical Systems
Geometric Topology
Probability
Abstract
For finitely supported random walks on finitely generated groups we prove that the identity map on extends to a continuous equivariant surjection from the Martin boundary to the Floyd boundary, with preimages of conical points being singletons. This yields new results for relatively hyperbolic groups. Our key estimate relates the Green and Floyd metrics, generalizing results of Ancona for random walks on hyperbolic groups and of Karlsson for quasigeodesics. We then apply these techniques to obtain some results concerning the harmonic measure on the limit sets of geometrically finite isometry groups of Gromov hyperbolic spaces. .
Keywords
Cite
@article{arxiv.1708.02133,
title = {Martin boundary covers Floyd boundary},
author = {Ilya Gekhtman and Victor Gerasimov and Leonid Potyagailo and Wenyuan Yang},
journal= {arXiv preprint arXiv:1708.02133},
year = {2017}
}