Ergodicity for the stochastic dynamics of quasi-invariant measures with applications to Gibbs states

DOI10.1006/jfan.1997.3099zbMath0892.60008OpenAlexW1987052046MaRDI QIDQ1370570

Yuri G. Kondratiev, Michael Roeckner, Sergio A. Albeverio

Publication date: 9 August 1998

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1997.3099

zbMATH Keywords

Gibbs statesquasi-invariant measuresextremalityEuclidean quantum field theoryclassical and quantum lattice modelsergodicity of measures w.r.t. shiftsergodicity of operator semigroups and of Markov processes/diffusionsirreducibility of Dirichlet forms

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Measure-preserving transformations (28D05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Ergodic theory (37A99)

Related Items (18)

Euclidean Gibbs measures on loop lattices: existence and a priori estimates. ⋮ A class of Lévy driven SDEs and their explicit invariant measures ⋮ Existence and a priori estimates for Euclidean Gibbs states ⋮ Restricted Markov uniqueness for the stochastic quantization of \(P(\Phi)_{2}\) and its applications ⋮ Unnamed Item ⋮ Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus ⋮ Ergodic decomposition of Dirichlet forms via direct integrals and applications ⋮ Sergio's work in statistical mechanics: from quantum particles to geometric stochastic analysis ⋮ A priori estimates for symmetrizing measures and their applications to Gibbs states ⋮ Irreducible recurrence, ergodicity, and extremality of invariant measures for resolvents ⋮ Ergodicity for the stochastic quantization problems on the 2D-torus ⋮ STOCHASTIC EQUATIONS AND DIRICHLET OPERATORS ON INFINITE PRODUCT MANIFOLDS ⋮ GLAUBER DYNAMICS FOR QUANTUM LATTICE SYSTEMS ⋮ Quasi-invariant measures and their characterization by conditional probabilities ⋮ Euclidean Gibbs measures of interacting quantum anharmonic oscillators ⋮ Stochastic analysis on product manifolds: Dirichlet operators on differential forms ⋮ Mosco convergence of Dirichlet forms in infinite dimensions with changing reference measures ⋮ A hierarchical model of quantum anharmonic oscillators: critical point convergence

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