Random walk speed is a proper function on Teichmüller space
Resumen:
Consider a closed surface M with negative Euler characteristic, and an admissible probability measure on the fundamental group of M with a 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.
| 2022 | |
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PIVOTING ARGUMENT SINGULARITY CONJETURE MATHEMATICS - GEOMETRIC TOPOLOGY MATHEMATICS -GROUPS THEORY MATHEMATICS - TOPOLOGY |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/44638 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| Sumario: | Versión permitida preprint. Publicado también en: Journal of Modern Dynamics, 2023, 19 : 815–832. DOI: 10.3934/jmd.2023022 |
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