On the local time of anisotropic random walk on Z^2

TL;DR

This paper investigates the local time of an anisotropic random walk on Z^2, providing precise asymptotic behavior of the probability of returning to the origin after N steps.

Contribution

It establishes the exact asymptotic behavior of the N-step return probability for anisotropic random walks on Z^2, advancing understanding of their long-term properties.

Findings

Derived the asymptotic behavior of return probabilities

Characterized the local time distribution for anisotropic walks

Enhanced understanding of anisotropic random walk dynamics

Abstract

We study the local time of the anisotropic random walk on the two-dimensional lattice Z^2, by establishing the exact asymptotic behavior of the N-step return probability to the origin.