Interacting elephant random walks

TL;DR

This paper investigates a class of interacting elephant random walks, revealing a first-order phase transition and condensation phenomena through simulations and theoretical analysis, with the transition point influenced by initial conditions.

Contribution

It introduces a new interacting model that generalizes the exclusion process and demonstrates phase transition behavior with initial condition dependence.

Findings

Exhibits a first-order phase transition.

Displays condensation phenomena.

Transition point depends on initial configuration.

Abstract

The elephant random walk is a history-dependent random walk. We study a class of interacting elephant random walks. Our model includes the exclusion process as a special case. By means of Monte Carlo simulations and mean-field arguments, we find that it exhibits a condensation phenomenon with a phase transition that is manifestly of first order. The transition point depends on the initial configuration.