About the distance between random walkers on some graphs

TL;DR

This paper studies the behavior of distances between multiple symmetric random walkers on various graphs, including the line, plane, and comb lattice, to understand their interaction and spatial properties.

Contribution

It introduces analysis of the distance dynamics among multiple symmetric random walks on different graph structures, expanding understanding beyond single-walker behavior.

Findings

Distances exhibit specific probabilistic properties depending on graph structure

Interactions between walkers influence their spatial distribution over time

Results vary across different graph types such as line, plane, and comb lattice

Abstract

We consider two or more simple symmetric walks on some graphs, e.g. the real line, the plane or the two dimensional comb lattice, and investigate the properties of the distance among the walkers.