映射类群上随机游动的拓扑熵
Topological Entropy of Random Walks on Mapping Class Groups
摘要：
对于亏格大于1的闭可定向曲面$S$上的任何伪Anosov同构，Bers和Thurston的工作已知拓扑熵与Teichmüller空间上关于Teichmüller度量的平移距离一致。本文研究了$S$映射类群上的随机游动。随机游动的漂移被定义为随机游动的平移距离。定义了随机游动的拓扑熵，并证明了它几乎必然与Teichmüller空间上关于Teichmüller度量的漂移一致.
英文摘要：
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.
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