Random walk speed is a proper function on Teichmüller space

Azemar, A., Gadre, V. , Gouëzel, S., Haettel, T., Lessa, P. and Uyanik, C. (2022) Random walk speed is a proper function on Teichmüller space. arXiv, (Unpublished)

Abstract

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.

• Item Type: Articles
• Status: Unpublished
• Refereed: No
• 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: arXiv