A remark on a central limit theorem for non-symmetric random walks on crystal lattices

TL;DR

This paper introduces a new central limit theorem for non-symmetric random walks on crystal lattices, expanding the theoretical understanding of their asymptotic behavior using a measure-change approach.

Contribution

It presents a novel type of central limit theorem for non-symmetric random walks on crystal lattices, utilizing a measure-change technique.

Findings

New central limit theorem established for non-symmetric random walks

Utilizes measure-change technique to prove the result

Extends previous work by Ishiwata, Kawabi, and Kotani

Abstract

Recently, Ishiwata, Kawabi and Kotani [2] proved two kinds of central limit theorems for non-symmetric random walks on crystal lattices from the view point of discrete geometric analysis. In the present paper, we obtain yet another kind of the central limit theorem for them. Our argument is based on a measure-change technique due to Alexopoulos [1].