Random walks and contracting elements II: Translation length and Quasi-isometric embedding

2022/12/23 by In-Hyeok Choi, Choi, Inhyeok · 1 citation
Mathematics · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2212.12119

Abstract

Continuing from a companion article: 'Random walks and contracting elements I: Deviation inequality and limit laws', we study random walks on metric spaces with contracting elements. We prove that random subgroups of the isometry group of a metric space is quasi-isometrically embedded into the space. We discuss this problem in two senses, namely, one involving random walks and the other involving counting problems. We also establish the genericity of contracting elements and the CLT and its converse for translation length.

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