收缩等距映射与逃逸率的可微性
群论
2025-10-14 v2 概率论
摘要
设G是一个其作用在度量空间X上涉及收缩等距映射的可数群。这一设置自然地包含作用于Gromov超曲面、Teichmüller空间、Culler-Vogtmann Outer space 和CAT(0)空间上的群。我们讨论了随机游走在G上的逃逸率的连续性和可微性。对于相对超曲面群、CAT(-1)群和CAT(0)立方群，我们进一步讨论了逃逸率的解析性。最后，假设G在X上的作用是弱properly discontinuous（WPD），我们讨论了随机游走在G上的渐近熵的连续性。
引用
@article{arxiv.2403.09992,
title = {Contracting isometries and differentiability of the escape rate},
author = {Inhyeok Choi},
journal= {arXiv preprint arXiv:2403.09992},
year = {2025}
}
备注
This paper contains (revised) part of the previously announced preprint 'Limit laws on Outer space, Teichm\"uller space, and CAT(0) spaces': arXiv:2207.06597v1 , which is now divided into several parts. v2, 50 pages, 1 figure. Version accepted by Probability Theory and Related Fields