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May 2019 Quenched central limit theorem rates of convergence for one-dimensional random walks in random environments
Sung Won Ahn, Jonathon Peterson
Bernoulli 25(2): 1386-1411 (May 2019). DOI: 10.3150/18-BEJ1024

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.

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Sung Won Ahn. Jonathon Peterson. "Quenched central limit theorem rates of convergence for one-dimensional random walks in random environments." Bernoulli 25 (2) 1386 - 1411, May 2019. https://doi.org/10.3150/18-BEJ1024

Information

Received: 1 April 2017; Revised: 1 November 2017; Published: May 2019
First available in Project Euclid: 6 March 2019

zbMATH: 07049410
MathSciNet: MR3920376
Digital Object Identifier: 10.3150/18-BEJ1024

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 2 • May 2019
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