LARGE DEVIATIONS FOR RANDOM WALKS ON HYPERBOLIC SPACES

Adrien Boulanger (1, 2) , Pierre Mathieu , Cagri Sert , Alessandro Sisto

1 CNRS - Centre National de la Recherche Scientifique
2 I2M - Institut de Mathématiques de Marseille

Let Γ be a countable group acting on a geodesic hyperbolic metric space X and µ a probability measure on Γ whose support generates a non-elementary semigroup. 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. One of the consequences of our results confirms a special case of a conjecture regarding large deviations of spectral radii of random matrix products.

Domaines: Mathématiques [math]

Adrien Boulanger, Pierre Mathieu, Cagri Sert, Alessandro Sisto. LARGE DEVIATIONS FOR RANDOM WALKS ON HYPERBOLIC SPACES. 2021. ⟨hal-03427257⟩