Exponential bounds for random walks on hyperbolic spaces without moment conditions

Sébastien Gouëzel

Type: Article

Publication Date: 2022-12-31

Citations: 12

DOI: https://doi.org/10.2140/tunis.2022.4.635

Abstract

We consider nonelementary random walks on general hyperbolic spaces. Without any moment condition on the walk, we show that it escapes linearly to infinity, with exponential error bounds. We even get such exponential bounds up to the rate of escape of the walk. Our proof relies on an inductive decomposition of the walk, recording times at which it could go to infinity in several independent directions, and using these times to control further backtracking.

Locations

Tunisian Journal of Mathematics - View
arXiv (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
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