Non-universality in clustered ballistic annihilation

TL;DR

This paper investigates a variant of ballistic annihilation with clustered stationary particles, revealing that the critical initial cluster density depends on both the mean and variance of cluster sizes, contrasting previous universality results.

Contribution

It introduces a clustered variant of ballistic annihilation and demonstrates that critical density depends on cluster size distribution, addressing an open question in the field.

Findings

Critical initial cluster density depends on mean and variance of cluster sizes.

Contrasts with previous universality results in ballistic annihilation.

Resolves an open question for coalescing ballistic annihilation.

Abstract

In ballistic annihilation, infinitely many particles with randomly assigned velocities move across the real line and mutually annihilate upon contact. We introduce a variant with superimposed clusters of multiple stationary particles. Our main result is that the critical initial cluster density to ensure species survival depends on both the mean and variance of the cluster size. Our result contrasts with recent ballistic annihilation universality findings with respect to particle spacings. A corollary of our theorem resolves an open question for coalescing ballistic annihilation.