Random walk speed is a proper function on Teichmüller space

Azemar, A., Gadre, V. , Gouëzel, S., Haettel, T., Lessa, P. and Uyanik, C. (2023) Random walk speed is a proper function on Teichmüller space. Journal of Modern Dynamics, 19, pp. 815-832. (doi: 10.3934/jmd.2023022) (Accepted for Publication)

Full text not currently available from Enlighten.

Abstract

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.

Item Type:Articles
Status:Accepted for Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Azemar, Mr Aitor and Gadre, Dr Vaibhav
Authors: Azemar, A., Gadre, V., Gouëzel, S., Haettel, T., Lessa, P., and Uyanik, C.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Modern Dynamics
Publisher:American Institute of Mathematical Sciences (AIMS)
ISSN:1930-5311
ISSN (Online):1930-532X
Related URLs:

University Staff: Request a correction | Enlighten Editors: Update this record