A priori estimates for symmetrizing measures and their applications to Gibbs states

DOI10.1006/jfan.1999.3482zbMath0968.60095OpenAlexW2018069628MaRDI QIDQ1975485

T. V. Tsykalenko, Yuri G. Kondratiev, Sergio A. Albeverio, Michael Roeckner

Publication date: 2 September 2001

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

Full work available at URL: https://doi.org/10.1006/jfan.1999.3482

zbMATH Keywords

configuration spaceGibbs measuremulti-body interactionlattice system

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Pseudodifferential operators and other generalizations of partial differential operators (35S99) Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) (46G99)

Related Items (9)

Euclidean Gibbs measures on loop lattices: existence and a priori estimates. ⋮ Invariance implies Gibbsian: some new results ⋮ Existence and a priori estimates for Euclidean Gibbs states ⋮ Gibbs states of interacting systems of quantum anharmonic oscillators ⋮ Sergio's work in statistical mechanics: from quantum particles to geometric stochastic analysis ⋮ On continuity equations in infinite dimensions with non-Gaussian reference measure ⋮ Quasi-invariant measures and their characterization by conditional probabilities ⋮ Euclidean Gibbs measures of interacting quantum anharmonic oscillators ⋮ Mosco convergence of Dirichlet forms in infinite dimensions with changing reference measures

Cites Work

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• Ergodicity of \(L^ 2\)-semigroups and extremality of Gibbs states
• Absolute continuity of smooth measures
• Decay of correlations in classical lattice models at high temperature
• A covariance estimate for Gibbs measures
• Compactness and the maximal Gibbs state for random Gibbs fields on a lattice
• Gibbs measures and phase transitions
• Random fields
• Étude des champs euclidiens sur un réseau \(\mathbb{Z}^nu\)
• Homogeneous random fields and statistical mechanics
• Differentiable measures and the Malliavin calculus
• Uniqueness of Gibbs states for quantum lattice systems
• Ergodicity for the stochastic dynamics of quasi-invariant measures with applications to Gibbs states
• Classical Dirichlet forms on topological vector spaces --- closability and a Cameron-Martin formula
• Dirichlet operators via stochastic analysis
• Convergence to equilibrium for classical and quantum spin systems
• Regularity of invariant measures on finite and infinite dimensional spaces and applications
• The strong decay to equilibrium for the stochastic dynamics of unbounded spin systems on a lattice
• Stochastic differential equations in infinite dimensions: Solutions via Dirichlet forms
• A Quasi-Invariance Theorem for Measures on Banach Spaces
• Stationary measures of stochastic gradient systems, infinite lattice models
• L 2 theory for the stochastic Ising model
• Existence and uniqueness of DLR measures for unbounded spin systems
• On uniqueness of invariant measures for finite- and infinite-dimensional diffusions
• A-priori estimates and existence of Gibbs measures: a simplified proof
• On the reconstruction of measures from their logarithmic derivatives
• Prescribing a System of Random Variables by Conditional Distributions

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