PUB - Publikationen an der Universität Bielefeld

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 E on L-2 (Gamma, mu) which corresponds to the generator H of the Glauber dynamics. We prove the existence of a Markov process M on F that is properly associated with S. In the case of a positive potential phi which satisfies delta := integral(R)(d) (1 - e(-phi(x)))zdx < 1, we also prove that the generator H has a spectral gap >= 1 - delta. Furthermore, for any pure Gibbs state A, we derive a Poincare inequality. The results about the spectral gap and the Poincare inequality are a generalization and a refinement of a recent result from [Ann. Inst. H. Poincare Probab. Statist. 38 (2002) 91-108]. (c) 2004 Elsevier SAS. All rights reserved.