Arrivals are universal in coalescing ballistic annihilation

TL;DR

This paper proves that in a coalescing ballistic annihilation system, the distribution of the first particle to reach the origin is independent of the initial spacing distribution, highlighting a universal arrival property.

Contribution

It establishes the universality of the first arrival time distribution in coalescing ballistic annihilation regardless of initial spacing laws.

Findings

First particle arrival time is distribution-independent.

Universal behavior observed across various coalescing rules.

Results apply to symmetric coalescing systems.

Abstract

Coalescing ballistic annihilation is an interacting particle system intended to model features of certain chemical reactions. Particles are placed with independent and identically distributed spacings on the real line and begin moving with velocities sampled from $-1,0,$ and $1$. Collisions result in either coalescence or mutual annihilation. For a variety of symmetric coalescing rules, we prove that the index of the first particle to arrive at the origin does not depend on the law for spacings between particles.