Ergodicity of L(2)-semigroups and extremality of Gibbs states

Albeverio S, Kondratiev Y, Röckner M (1997)
JOURNAL OF FUNCTIONAL ANALYSIS 144(2): 394-423.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
We extend the classical results of Holley-Stroock on the characterization of extreme Gibbs states for the Ising model in terms of the irreducibility (resp. ergodicity) of the corresponding Glauber dynamics to the case of lattice systems with unbounded (linear) spin spaces. We first develop a general Framework to discuss questions of this type using classical Dirichlet forms on infinite dimensional state spaces and their associated diffusions. We then describe concrete applications to lattice models with polynomial interactions (i.e., the discrete P(phi)(d)-models of Euclidean quantum field theory). In addition, we prove the equivalence of extremality and shift-ergodicity for tempered Gibbs states of these models and also discuss this question in the general framework. (C) 1997 Academic Press.
Erscheinungsjahr
Zeitschriftentitel
JOURNAL OF FUNCTIONAL ANALYSIS
Band
144
Ausgabe
2
Seite(n)
394-423
ISSN
PUB-ID

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Albeverio S, Kondratiev Y, Röckner M. Ergodicity of L(2)-semigroups and extremality of Gibbs states. JOURNAL OF FUNCTIONAL ANALYSIS. 1997;144(2):394-423.
Albeverio, S., Kondratiev, Y., & Röckner, M. (1997). Ergodicity of L(2)-semigroups and extremality of Gibbs states. JOURNAL OF FUNCTIONAL ANALYSIS, 144(2), 394-423.
Albeverio, S., Kondratiev, Y., and Röckner, M. (1997). Ergodicity of L(2)-semigroups and extremality of Gibbs states. JOURNAL OF FUNCTIONAL ANALYSIS 144, 394-423.
Albeverio, S., Kondratiev, Y., & Röckner, M., 1997. Ergodicity of L(2)-semigroups and extremality of Gibbs states. JOURNAL OF FUNCTIONAL ANALYSIS, 144(2), p 394-423.
S. Albeverio, Y. Kondratiev, and M. Röckner, “Ergodicity of L(2)-semigroups and extremality of Gibbs states”, JOURNAL OF FUNCTIONAL ANALYSIS, vol. 144, 1997, pp. 394-423.
Albeverio, S., Kondratiev, Y., Röckner, M.: Ergodicity of L(2)-semigroups and extremality of Gibbs states. JOURNAL OF FUNCTIONAL ANALYSIS. 144, 394-423 (1997).
Albeverio, Sergio, Kondratiev, Yuri, and Röckner, Michael. “Ergodicity of L(2)-semigroups and extremality of Gibbs states”. JOURNAL OF FUNCTIONAL ANALYSIS 144.2 (1997): 394-423.