A note on dispersing particles on a line

TL;DR

This paper analyzes a particle dispersion process on an infinite line, demonstrating that the final occupied set scales linearly with the number of particles involved, providing insights into the process's spatial efficiency.

Contribution

It establishes that the final occupied sites in the dispersion process on an infinite line are proportional to the number of particles, offering a new understanding of the process's spatial characteristics.

Findings

Final occupied sites are O(n) in size.

The process efficiently disperses particles over the line.

Provides bounds on the spatial extent of dispersion.

Abstract

We consider a synchronous dispersion process introduced in \cite{CRRS} and we show that on the infinite line the final set of occupied sites takes up $O(n)$ space, where $n$ is the number of particles involved.