Exact encounter times for many random walkers on regular and complex networks

TL;DR

This paper derives exact formulas for the mean encounter times of multiple random walkers on various networks, considering both independent and exclusion-interaction scenarios, validated by simulations.

Contribution

It provides the first analytical solutions for encounter times in systems with many walkers on regular and complex networks, including exclusion effects.

Findings

Analytical formulas match simulation results closely.

Encounter times depend on network topology and walker interactions.

Results applicable to modeling diffusion and spreading processes.

Abstract

The exact mean time between encounters of a given particle in a system consisting of many particles undergoing random walks in discrete time is calculated, on both regular and complex networks. Analytical results are obtained both for independent walkers, where any number of walkers can occupy the same site, and for walkers with an exclusion interaction, when no site can contain more than one walker. These analytical results are then compared with numerical simulations, showing very good agreement.