Yet Another Condition for Absence of Collisions for Competing Brownian Particles

TL;DR

This paper introduces a new, simple condition ensuring no multiple collisions occur in finite and infinite systems of rank-based competing Brownian particles, extending previous results to broader cases.

Contribution

It provides a novel sufficient condition for collision absence that applies to both finite and infinite particle systems, advancing the understanding of their dynamics.

Findings

Condition guarantees no multiple collisions of a given order

Applicable to both finite and infinite particle systems

Extends previous collision criteria to infinite systems

Abstract

Consider a finite system of rank-based competing Brownian particles, where the drift and diffusion of each particle depend only on its current rank relative to other particles. We present a simple sufficient condition for absence of multiple collisions of a given order, continuing the earlier work by Bruggeman and Sarantsev (2015). Unlike in that paper, this new condition works even for infinite systems.