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arXiv · 2008.02709

Large deviations for random walks on Gromov-hyperbolic spaces

Adrien Boulanger·Pierre Mathieu·Cagri Sert·Alessandro Sisto
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Abstract

Let $\Gamma$ be a countable group acting on a geodesic Gromov-hyperbolic metric space $X$ and $\mu$ a probability measure on $\Gamma$ whose support generates a non-elementary subsemigroup. Under the assumption that $\mu$ has a finite exponential moment, we establish large deviations results for the distance and the translation length of a random walk with driving measure $\mu$. From our results, we deduce a special case of a conjecture regarding large deviations of spectral radii of random matrix products.

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Adrien Boulanger, Pierre Mathieu, Cagri Sert, Alessandro Sisto. 2020-08-05. Large deviations for random walks on Gromov-hyperbolic spaces. https://arxiv.org/abs/2008.02709

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