Glauber dynamics of continuous particle systems

Details Glauber dynamics of continuous particle systems Glauber dynamics of continuous particle systems

2003-06-17

arxiv.org/abs/math/0306252v1

Mathematics

Probability

Scientific paper

This paper is devoted to the construction and study of an equilibrium Glauber-type dynamics of infinite continuous particle systems. This dynamics is a special case of a spatial birth and death process. On the space $\Gamma$ of all locally finite subsets (configurations) in ${\Bbb R}^d$, we fix a Gibbs measure $\mu$ corresponding to a general pair potential $\phi$ and activity $z>0$. We consider a Dirichlet form $ \cal E$ on $L^2(\Gamma,\mu)$ which corresponds to the generator $H$ of the Glauber dynamics. We prove the existence of a Markov process $\bf M$ on $\Gamma$ that is properly associated with $\cal E$. In the case of a positive potential $\phi$ which satisfies $\delta{:=}\int_{{\Bbb R}^d}(1-e^{-\phi(x)}) z dx<1$, we also prove that the generator $H$ has a spectral gap $\ge1-\delta$. Furthermore, for any pure Gibbs state $\mu$, we derive a Poincar\'e inequality. The results about the spectral gap and the Poincar\'e inequality are a generalization and a refinement of a recent result by L. Bertini, N. Cancrini, and F. Cesi.

Affiliated with

Also associated with

No associations

Rating

Glauber dynamics of continuous particle systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Glauber dynamics of continuous particle systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Glauber dynamics of continuous particle systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-265507