Contracting isometries and differentiability of the escape rate
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911204452073472 |
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| author | Choi, Inhyeok |
| author_facet | Choi, Inhyeok |
| contents | Let $G$ be a countable group whose action on a metric space $X$ involves a contracting isometry. This setting naturally encompasses groups acting on Gromov hyperbolic spaces, Teichm{ü}ller space, Culler-Vogtmann Outer space and CAT(0) spaces. We discuss continuity and differentiability of the escape rate of random walks on $G$. For relatively hyperbolic groups, CAT(-1) groups and CAT(0) cubical groups, we further discuss analyticity of the escape rate. Finally, assuming that the action of $G$ on $X$ is weakly properly discontinuous (WPD), we discuss continuity of the asymptotic entropy of random walks on $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09992 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Contracting isometries and differentiability of the escape rate Choi, Inhyeok Group Theory Probability Let $G$ be a countable group whose action on a metric space $X$ involves a contracting isometry. This setting naturally encompasses groups acting on Gromov hyperbolic spaces, Teichm{ü}ller space, Culler-Vogtmann Outer space and CAT(0) spaces. We discuss continuity and differentiability of the escape rate of random walks on $G$. For relatively hyperbolic groups, CAT(-1) groups and CAT(0) cubical groups, we further discuss analyticity of the escape rate. Finally, assuming that the action of $G$ on $X$ is weakly properly discontinuous (WPD), we discuss continuity of the asymptotic entropy of random walks on $G$. |
| title | Contracting isometries and differentiability of the escape rate |
| topic | Group Theory Probability |
| url | https://arxiv.org/abs/2403.09992 |