A note on equilibrium Glauber and Kawasaki dynamics for permanental point processes

zbMATH Open1240.60262arXiv1005.4537MaRDI QIDQ3091094

Guanhua Li, Eugene Lytvynov

Publication date: 8 September 2011

Abstract: We construct two types of equilibrium dynamics of an infinite particle system in a locally compact metric space $X$ for which a permanental point process is a symmetrizing, and hence invariant measure. The Glauber dynamics is a birth-and-death process in $X$, while in the Kawasaki dynamics interacting particles randomly hop over $X$. In the case $X=mathbb{R}^d$, we consider a diffusion approximation for the Kawasaki dynamics at the level of Dirichlet forms. This leads us to an equilibrium dynamics of interacting Brownian particles for which a permanental point process is a symmetrizing measure.

Full work available at URL: https://arxiv.org/abs/1005.4537

zbMATH Keywords

Dirichlet formGlauber dynamicsKawasaki dynamicspermanental point processes

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Diffusion processes (60J60) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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