Hitting times and periodicity in random dynamics

TL;DR

This paper establishes laws governing the time it takes for random dynamical systems to hit certain states, revealing a fundamental difference between periodic and non-periodic points, with implications for random Gibbs measures.

Contribution

It introduces a dichotomy in hitting time laws for periodic versus non-periodic points in random subshifts of finite type, extending to random Gibbs measures.

Findings

Hitting time laws differ for periodic and non-periodic points.

A dichotomy in hitting time statistics is established.

Results apply to random Gibbs measures.

Abstract

We prove quenched laws of hitting time statistics for random subshifts of finite type. In particular we prove a dichotomy between the law for periodic and for non-periodic points. We show that this applies to random Gibbs measures.