# Quenched central limit theorem rates of convergence for one-dimensional random walks in random environments

## TL;DR

This paper establishes polynomial rates of convergence for quenched central limit theorems in one-dimensional RWRE, providing quantitative bounds on how quickly the walk's distribution approaches its limit under fixed environments.

## Contribution

It offers new upper bounds on the convergence rates for quenched CLTs in 1D RWRE, depending on the environment distribution, advancing understanding of their asymptotic behavior.

## Key findings

- Polynomial convergence rates depend on environment distribution
- Upper bounds are provided for hitting time and position CLTs
- Results improve quantitative understanding of RWRE limit behaviors

## Abstract

Unlike classical simple random walks, one-dimensional random walks in random environments (RWRE) are known to have a wide array of potential limiting distributions. Under certain assumptions, however, it is known that CLT-like limiting distributions hold for the walk under both the quenched and averaged measures. We give upper bounds on the rates of convergence for the quenched central limit theorems for both the hitting time and position of the RWRE with polynomial rates of convergence that depend on the distribution on environments.