Abstract
Abstract
In this paper we study the quenched distributions of hitting times for a class of random dynamical systems. We prove that hitting times to dynamically defined cylinders converge to a Poisson point process under the law of random equivariant measures with super-polynomial decay of correlations. In particular, we apply our results to uniformly aperiodic random subshifts of finite type equipped with random invariant Gibbs measures. We emphasize that we make no assumptions about the mixing property of the marginal measure.
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Reference25 articles.
1. Inequalities for the occurrence times of rare events in mixing processes. The state of the art;Abadi;Markov Process. Relat. Fields,2001
2. Annealed and quenched limit theorems for random expanding dynamical systems;Aimino;Probab. Theory Relat. Fields,2015
3. Laws of rare events for deterministic and random dynamical systems;Aytaç;Trans. Am. Math. Soc.,2015
4. Quenched CLT for random toral automorphism;Ayyer;Discrete Continuous Dyn. Syst.,2009
5. Exponential decay of correlations for randomly chosen hyperbolic toral automorphisms;Ayyer;Chaos,2007