Random walks and contracting elements III: Outer space and outer automorphism group
Abstract
Continuing from the author's previous article 'Random walks and contracting elements I', we study random walks on (possibly asymmetric) metric spaces using the bounded geodesic image property (BGIP) of certain isometries. As an application, we show that a generic outer automorphism of the free group of rank at least 3 has different forward and backward expansion factors. This answers a question of Handel and Mosher.
Cite
@article{arxiv.2212.12122,
title = {Random walks and contracting elements III: Outer space and outer automorphism group},
author = {Inhyeok Choi},
journal= {arXiv preprint arXiv:2212.12122},
year = {2024}
}
Comments
This is the third 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. 40 pages. v2: updated the exposition following the revision of the previous two papers in the series. Comments are welcome! arXiv admin note: text overlap with arXiv:2207.06597