Topological Entropy of Random Walks on Mapping Class Groups
Geometric Topology
2017-01-30 v2
Abstract
For any pseudo-Anosov diffeomorphism on a closed orientable surface of genus greater than one, it is known by the work of Bers and Thurston that the topological entropy agrees with the translation distance on the Teichm\"uller space with respect to the Teichm\"uller metric. In this paper, we consider random walks on the mapping class group of . The drift of a random walk is defined as the translation distance of the random walk. We define the topological entropy of a random walk and prove that it almost surely agrees with the drift on the Teichm\"uller space with respect to the Teichm\"uller metric.
Cite
@article{arxiv.1604.00749,
title = {Topological Entropy of Random Walks on Mapping Class Groups},
author = {Hidetoshi Masai},
journal= {arXiv preprint arXiv:1604.00749},
year = {2017}
}
Comments
16 pages, 1 figure. Comments are welcome, v3 only title has been changed from v2, see also version published in IMRN