The Global Evolution of States of a Continuum Kawasaki Model with Repulsion

TL;DR

This paper constructs and analyzes the long-term evolution of a continuum particle system with repulsion, demonstrating that sub-Poissonian states are preserved over time using correlation functions.

Contribution

It provides a rigorous method to evolve states of a continuum Kawasaki model with repulsion, ensuring sub-Poissonian properties are maintained for all time.

Findings

Global in time evolution of states constructed

Sub-Poissonian states are preserved over time

Correlation functions used to analyze the system

Abstract

An infinite system of point particles performing random jumps in $\mathds{R}^d$ with repulsion is studied. The states of the system are probability measures on the space of particle's configurations. The result of the paper is the construction of the global in time evolution of states with the help of the corresponding correlation functions. It is proved that for each initial sub-Poissonian state $\mu_0$, the constructed evolution $\mu_0 \mapsto \mu_t$ preserves this property. That is, $\mu_t$ is sub-Poissonian for all $t>0$.