## Bernoulli

• Bernoulli
• Volume 25, Number 2 (2019), 1386-1411.

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

#### 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.

#### Article information

Source
Bernoulli, Volume 25, Number 2 (2019), 1386-1411.

Dates
Revised: November 2017
First available in Project Euclid: 6 March 2019

https://projecteuclid.org/euclid.bj/1551862854

Digital Object Identifier
doi:10.3150/18-BEJ1024

Mathematical Reviews number (MathSciNet)
MR3920376

Zentralblatt MATH identifier
07049410

#### Citation

Ahn, Sung Won; Peterson, Jonathon. Quenched central limit theorem rates of convergence for one-dimensional random walks in random environments. Bernoulli 25 (2019), no. 2, 1386--1411. doi:10.3150/18-BEJ1024. https://projecteuclid.org/euclid.bj/1551862854

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