Exponential bounds for random walks on hyperbolic spaces without moment conditions
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Publication:6359630
DOI10.2140/TUNIS.2022.4.635arXiv2102.01408MaRDI QIDQ6359630
Publication date: 2 February 2021
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.
Large deviations (60F10) Hyperbolic groups and nonpositively curved groups (20F67) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Probabilistic methods in group theory (20P05)
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