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Glauber dynamics of continuous particle systems.
| Content Provider | CiteSeerX |
|---|---|
| Author | Kondratiev, Yuri Lytvynov, Eugene |
| 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 Γ of all locally finite subsets (configurations) in Rd, we fix a Gibbs measure µ corresponding to a general pair potential φ and activity z> 0. We consider a Dirichlet form E on L2 (Γ,µ) which corresponds to the generator H of the Glauber dynamics. We prove the existence of a Markov process M on Γ that is properly associated with E. In the case of a positive potential φ which satisfies δ: = ∫ Rd(1 − e−φ(x))z dx < 1, we also prove that the generator H has a spectral gap ≥ 1−δ. Furthermore, for any pure Gibbs state µ, we derive a Poincaré inequality. The results about the spectral gap and the Poincaré inequality are a generalization and a refinement of a recent result from [6]. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Glauber Dynamic Continuous Particle System Poincar Inequality Spectral Gap Death Process Markov Process Pure Gibbs State General Pair Dirichlet Form Spatial Birth Infinite Continuous Particle System Gibbs Measure Equilibrium Glauber-type Dynamic Positive Potential Special Case Finite Subset Recent Result |
| Content Type | Text |
| Resource Type | Article |
