Glauber dynamics of continuous particle systems

摘要: Abstract This paper is devoted to the construction and study of an equilibrium Glauber-type dynamics infinite continuous particle systems. a special case spatial birth death process. On space Γ all locally finite subsets (configurations) in R d , we fix Gibbs measure μ corresponding general pair potential ϕ activity z > 0 . We consider Dirichlet form E on L 2 ( ) which corresponds generator H Glauber dynamics. prove existence Markov process M that properly associated with In positive satisfies δ : = ∫ 1 − e x also has spectral gap ⩾ Furthermore, for any pure state μ, derive Poincare inequality. The results about inequality are generalization refinement recent result from [Ann. Inst. H. Probab. Statist. 38 (2002) 91–108].