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- W2950807908 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 ${Bbb R}^d$, 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." @default.
- W2950807908 created "2019-06-27" @default.
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- W2950807908 date "2003-06-17" @default.
- W2950807908 modified "2023-09-27" @default.
- W2950807908 title "Glauber dynamics of continuous particle systems" @default.
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