2016/04/04 by Hidetoshi Masai, Masai, Hidetoshi
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1604.00749
openalex publication_date 2016/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any pseudo-Anosov diffeomorphism 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 paper, 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.