Diffusion coefficients for multi-step persistent random walks on lattices

TL;DR

This paper presents a method to calculate diffusion coefficients for multi-step persistent random walks on various lattices, accounting for memory effects in the walker's movement.

Contribution

It introduces a simple approach to derive explicit diffusion coefficients for two-step memory walks across different lattice types and dimensions.

Findings

Explicit formulas for diffusion coefficients on various lattices

Method applicable to walks with two-step memory

Enhanced understanding of persistent random walk behavior

Abstract

We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with two-step memory on different classes of one-, two- and higher-dimensional lattices.