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Exponential bounds
for random walks on hyperbolic spaces without moment
conditions
Sébastien Gouëzel |
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Vol. 4 (2022), No. 4, 635–671
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Abstract |
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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 escape rate 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. |
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Keywords
large deviations, random walks, hyperbolic groups
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Mathematical Subject Classification
Primary: 20F67, 20P05, 60B15, 60F10
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Milestones
Received: 15 February 2021
Revised: 28 April 2022
Accepted: 1 June 2022
Published: 15 January 2023
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Authors |
| Sébastien Gouëzel | |
| IRMAR, CNRS UMR 6625 Université de Rennes 1 Rennes France |
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