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

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 $t>0$.