Harmonic measures versus quasiconformal measures for hyperbolic groups
Probability
2013-02-11 v2 Group Theory
Metric Geometry
Abstract
We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as \qc measures on the boundary of the group.
Cite
@article{arxiv.0806.3915,
title = {Harmonic measures versus quasiconformal measures for hyperbolic groups},
author = {Sébastien Blachère and Peter Haïssinsky and Pierre Mathieu},
journal= {arXiv preprint arXiv:0806.3915},
year = {2013}
}
Comments
Besides minor modifications, we provide a new proof that the harmonic measure of a finitely supported random walk on a Fuchsian group with cusps is singular. 52 pp