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

2010/05/25 by Guanhua Li, Li, Guanhua, Eugene Lytvynov +1
Mathematics · #60F99 #60J60 #60J75 #60J80 #60K35 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60F99 #msc:60J60 #msc:60J75 #msc:60J80 #msc:60K35

paper · pdf · doi:10.48550/arxiv.1005.4537

openalex publication_date 2010/05/25 · arxiv created 2010/12/09 · arxiv updated 2010/12/10 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

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.

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