Harmonic measures for distributions with finite support on the mapping class group are singular
Geometric Topology
2015-01-14 v2 Dynamical Systems
Abstract
Kaimanovich and Masur showed that a random walk on the mapping class group for an initial distribution with finite first moment and whose support generates a non-elementary subgroup, converges almost surely to a point in the space PMF of projective measured foliations on the surface. This defines a harmonic measure on PMF. Here, we show that when the initial distribution has finite support, the corresponding harmonic measure is singular with respect to the natural Lebesgue measure on PMF.
Keywords
Cite
@article{arxiv.0911.2891,
title = {Harmonic measures for distributions with finite support on the mapping class group are singular},
author = {Vaibhav S Gadre},
journal= {arXiv preprint arXiv:0911.2891},
year = {2015}
}
Comments
43 pages, 16 figures. Minor improvements overall, specifically Section 12. Added references