Long time behavior of stochastic hard ball systems

TL;DR

This paper investigates the long-term dynamics of systems with two or three Brownian hard balls in multi-dimensional space, focusing on how mutual attraction and elastic collisions influence their behavior over time.

Contribution

It provides new insights into the asymptotic behavior of small stochastic hard ball systems under attraction and elastic collisions.

Findings

Analysis of long-time behavior for 2 and 3 balls

Effects of attraction and collisions on system stability

Characterization of equilibrium states or recurrence

Abstract

We study the long time behavior of a system of $n=2,3$ Brownian hard balls, living in $\mathbb{R}^d$ for $d\ge2$, submitted to a mutual attraction and to elastic collisions.