Random Young Towers and Quenched Limit Laws

TL;DR

This paper establishes a quenched almost sure invariance principle with a convergence rate for Random Young Towers and applies it to i.i.d perturbations of non-uniformly expanding maps, addressing an open question in the field.

Contribution

It introduces a quenched invariance principle with convergence rate for Random Young Towers and extends the results to perturbed non-uniformly expanding maps.

Findings

Proves quenched invariance principle with convergence rate for Random Young Towers.

Applies the theory to i.i.d perturbations of non-uniformly expanding maps.

Answers an open question from previous research.

Abstract

We obtain quenched almost sure invariance principle (with convergence rate) for Random Young Tower. We apply our result to i.i.d perturbations of non-uniformly expanding maps. In particular, we answer one open question in \cite{BBM}.