Random walk speed is a proper function on Teichmüller space
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866911914629529600 |
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| author | Azemar, Aitor Gadre, Vaibhav Gouëzel, Sébastien Haettel, Thomas Lessa, Pablo Uyanik, Caglar |
| author_facet | Azemar, Aitor Gadre, Vaibhav Gouëzel, Sébastien Haettel, Thomas Lessa, Pablo Uyanik, Caglar |
| contents | Consider a closed surface $M$ with negative Euler characteristic, and an admissible probability measure on the fundamental group of $M$ with finite first moment. Corresponding to each point in the Teichmüller space of $M$, there is an associated random walk on the hyperbolic plane. We show that the speed of this random walk is a proper function on the Teichmüller space of $M$, and we relate the growth of the speed to the Teichmüller distance to a basepoint. One key argument is an adaptation of Gouëzel's pivoting techniques to actions of a fixed group on a sequence of hyperbolic metric spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2212_06581 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Random walk speed is a proper function on Teichmüller space Azemar, Aitor Gadre, Vaibhav Gouëzel, Sébastien Haettel, Thomas Lessa, Pablo Uyanik, Caglar Geometric Topology Group Theory Probability 05C81, 60B20, 20F67, 30F45, 20E08 Consider a closed surface $M$ with negative Euler characteristic, and an admissible probability measure on the fundamental group of $M$ with finite first moment. Corresponding to each point in the Teichmüller space of $M$, there is an associated random walk on the hyperbolic plane. We show that the speed of this random walk is a proper function on the Teichmüller space of $M$, and we relate the growth of the speed to the Teichmüller distance to a basepoint. One key argument is an adaptation of Gouëzel's pivoting techniques to actions of a fixed group on a sequence of hyperbolic metric spaces. |
| title | Random walk speed is a proper function on Teichmüller space |
| topic | Geometric Topology Group Theory Probability 05C81, 60B20, 20F67, 30F45, 20E08 |
| url | https://arxiv.org/abs/2212.06581 |