Recurrence of the plane Elephant random walk

TL;DR

This paper provides a simple proof of the recurrence property of the two-dimensional elephant random walk in the diffusive regime, using basic comparison techniques with standard random walks.

Contribution

It introduces a straightforward proof method for recurrence, potentially applicable to other complex stochastic processes.

Findings

Proves recurrence of 2D elephant random walk in diffusive regime

Uses rough comparison with standard plane random walk

Simplifies previous proofs by Shuo Qin

Abstract

We give a short proof of the recurrence of the two-dimensional elephant random walk in the diffusive regime. This was recently established by Shuo Qin, but our proof only uses very rough comparison with the standard plane random walk. We hope that the method can be useful for other applications.