Quenched Poisson processes for random subshifts of finite type

TL;DR

This paper investigates the distribution of hitting times in random dynamical systems, showing convergence to a Poisson process under certain conditions, with applications to random subshifts of finite type.

Contribution

It establishes convergence of hitting times to a Poisson process for random subshifts of finite type without requiring mixing assumptions.

Findings

Hitting times converge to a Poisson point process.

Results apply to random subshifts with Gibbs measures.

No mixing assumptions needed for the marginal measure.

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.