Year: 2025
Type: article
Abstract: Let G be a group acting on a CAT ( 0 ) space with contracting isometries. We study the random walk generated by an admissible measure on G . We prove that if the action is non-elementary and under optimal moment assumptions on the measure, the random walk satisfies a central limit theorem. The general approach is inspired from the cocycle argument of Y. Benoist and J-F. Quint, and our strategy relies on the use of hyperbolic models introduced by H. Petyt, A. Zalloum and D. Spriano, which are analogues of the contact graph for the class of CAT ( 0 ) spaces. As a side result, we prove that the probability that the n th-step the random walk acts as a contracting isometry goes to 1 as n goes to infinity.
Source: Annales de l’institut Fourier
DOI: 10.5802/aif.3717
Author: Corentin Le Bars
Institution: Weizmann Institute of Science
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411373859