Glauber dynamics of continuous particle systems

Kondratiev Y, Lytvynov E (2005)
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 41(4): 685-702.

Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Zeitschriftenaufsatz | Veröffentlicht | Englisch
Autor
;
Abstract / Bemerkung
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.
Erscheinungsjahr
Zeitschriftentitel
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
Band
41
Ausgabe
4
Seite(n)
685-702
ISSN
PUB-ID

Zitieren

Kondratiev Y, Lytvynov E. Glauber dynamics of continuous particle systems. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. 2005;41(4):685-702.
Kondratiev, Y., & Lytvynov, E. (2005). Glauber dynamics of continuous particle systems. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 41(4), 685-702. doi:10.1016/j.anihpb.2004.05.002
Kondratiev, Y., and Lytvynov, E. (2005). Glauber dynamics of continuous particle systems. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 41, 685-702.
Kondratiev, Y., & Lytvynov, E., 2005. Glauber dynamics of continuous particle systems. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 41(4), p 685-702.
Y. Kondratiev and E. Lytvynov, “Glauber dynamics of continuous particle systems”, ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, vol. 41, 2005, pp. 685-702.
Kondratiev, Y., Lytvynov, E.: Glauber dynamics of continuous particle systems. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. 41, 685-702 (2005).
Kondratiev, Yuri, and Lytvynov, Eugene. “Glauber dynamics of continuous particle systems”. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 41.4 (2005): 685-702.