2018/12/17 by Hidetoshi Masai, Masai, Hidetoshi
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1812.06651
openalex publication_date 2018/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A random walk on a countable group G acting on a metric space X gives a characteristic called the drift which depends only on the transition probability measure μ of the random walk. The drift is the `translation distance' of the random walk. In this paper, we prove that the drift varies continuously with the transition probability measures, under the assumption that the distance and the horofunctions on X are expressed by certain ratios. As an example, we consider the mapping class group MCG(S) acting on the Teichmüller space. By using north-south dynamics, we also consider the continuity of the drift for a sequence converging to a Dirac measure. As an appendix, we prove that the asymptotic entropy of the random walks on MCG(S) varies continuously.