Functional limit theorems for elephant random walks on general periodic structures

TL;DR

This paper extends functional limit theorems for Elephant Random Walks to general periodic structures, revealing how underlying structures influence asymptotic behavior beyond classical lattice settings.

Contribution

It introduces new structure-dependent quantities affecting the asymptotic behavior of ERWs on periodic structures, generalizing previous results on $\

Findings

New structure-dependent quantities identified

Asymptotic behavior influenced by underlying periodic structure

Extension of Bertenghi's results to broader settings

Abstract

This paper investigates functional limit theorems for the Elephant Random Walk (ERW) on general periodic structures, extending the Bertenghi's results on $\mathbb{Z}^d$. Our results reveal new structure-dependent quantities that do not appear in the classical setting $\mathbb{Z}^d$, highlighting how the underlying structure affects the asymptotic behavior of the walk.