Infinite particle systems with hard-core and long-range interaction

TL;DR

This paper studies infinite systems of particles with hard-core and long-range interactions, modeling them as reflecting Brownian motions and proving existence and uniqueness of solutions to the associated infinite-dimensional equations.

Contribution

It extends the theory of reflecting Brownian motions to infinite particle systems with long-range interactions, establishing existence and uniqueness results.

Findings

Proved existence of strong solutions for infinite particle systems.

Established uniqueness of solutions under specified conditions.

Analyzed the impact of long-range interactions on system dynamics.

Abstract

A system of Brownian hard balls is regarded as a reflecting Brownian motion in the configuration space and can be represented by a solution to a Skorohod-type equation. In this article, we consider the case that there are an infinite number of balls, and the interaction between balls is given by the long-range pair interaction. We discuss the existence and uniqueness of strong solutions to the infinite-dimensional Skorohod equation.