Random walks and contracting elements II: Translation length and Quasi-isometric embedding
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.
Keywords
Cite
@article{arxiv.2212.12119,
title = {Random walks and contracting elements II: Translation length and Quasi-isometric embedding},
author = {Inhyeok Choi},
journal= {arXiv preprint arXiv:2212.12119},
year = {2025}
}
Comments
This is the second of a series of articles reformulating the author's previous article 'Limit laws on Outer space, Teichm\"uller space, and CAT(0) spaces": arXiv:2207.06597v1. 47 pages. The final version will appear in Groups, Geometry, and Dynamics