Harmonic measures versus quasiconformal measures for hyperbolic groups

Details Harmonic measures versus quasiconformal measures for hyperbolic groups Harmonic measures versus quasiconformal measures for hyperbolic groups

2008-06-24

arxiv.org/abs/0806.3915v2

Mathematics

Probability

Besides minor modifications, we provide a new proof that the harmonic measure of a finitely supported random walk on a Fuchsia

Scientific paper

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.

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