Random Walk on Lattice with an Antisymmetric Perturbation in One Point

TL;DR

This paper analyzes a random walk on a lattice with a localized antisymmetric perturbation, providing exact asymptotic corrections to its diffusive behavior, advancing understanding of localized effects in stochastic processes.

Contribution

It introduces an exact calculation of spatial corrections for a lattice random walk with a point-specific antisymmetric perturbation, extending local limit theorem applications.

Findings

Derived explicit asymptotic probability corrections

Demonstrated impact of localized antisymmetric perturbation

Extended local limit theorem to perturbed lattice walks

Abstract

We study an homogeneous irreducible markovian random walk in a square lattice of arbitrary dimension, with an antisymmetric perturbation acting only in one point. We compute exactly spatial correction to the diffusive behaviour in the asympotics of probability, in the spirit of local limit theorems for random walks.