Open Access

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

### 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.

### Article Information

 Title A note on equilibrium Glauber and Kawasaki dynamics for permanental point processes Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 1, 29-46 MathSciNet MR2815373 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

Guanhua Li
Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K.

Eugene Lytvynov
Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K.

### Citation Example

Guanhua Li and Eugene Lytvynov, A note on equilibrium Glauber and Kawasaki dynamics for permanental point processes, Methods Funct. Anal. Topology 17 (2011), no. 1, 29-46.

### BibTex

@article {MFAT563,
AUTHOR = {Li, Guanhua and Lytvynov, Eugene},
TITLE = {A note on equilibrium Glauber and Kawasaki dynamics for permanental point processes},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {1},
PAGES = {29-46},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=563},
}