Yu. Kondratiev, E.Lytvynov
Glauber dynamics of continuous particle systems
(62K, LATeX 2e)

ABSTRACT.  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 $\R^d$, 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 
$\delta{:=}\int_{\R^d}(1-e^{-\phi(x)})\, z\, dx<1$, 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 of L. Bertini, N. Cancrini, and F. Cesi.