Topological entropy of random walks on mapping class groups

Hidetoshi Masai

Research output: Contribution to journalArticlepeer-review

Abstract

For any pseudo-Anosov homeomorphism on a closed orientable surface S 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 Teichmüller space with respect to the Teichmüller metric. In this article, we consider random walks on the mapping class group of S. 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 Teichmüller space with respect to the Teichmüller metric.

Original languageEnglish
Pages (from-to)739-761
Number of pages23
JournalInternational Mathematics Research Notices
Volume2018
Issue number3
DOIs
Publication statusPublished - 2018

ASJC Scopus subject areas

  • Mathematics(all)

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