Large deviations for random walks on Gromov-hyperbolic spaces

Adrien Boulanger, Pierre Mathieu, Cagri Sert, Alessandro Sisto

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Let Γ be a countable group acting on a geodesic Gromov-hyperbolic metric space X and μ a probability measure on Γ whose support generates a non-elementary subsemigroup. Under the assumption that μ has a finite exponential moment, we establish large deviations results for the distance and the translation length of a random walk with driving measure μ. From our results, we deduce a special case of a conjecture regarding large deviations of spectral radii of random matrix products.
Original languageEnglish
Pages (from-to)885-944
Number of pages60
JournalAnnales scientifiques de l'École normale supérieure
Issue number3
Publication statusPublished - May 2023


  • math.PR
  • math.DS
  • math.GR
  • math.GT


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