Putan, Diana: Uniqueness of equilibrium states in some models of interacting particle systems. 2014
Inhalt
- 1 Introduction
- 2 General Theory: Uniqueness Problem for Gibbs Measures
- 2.1 Formulation of the Uniqueness Problem
- 2.1.1 Basic notions in Graph Theory
- 2.1.2 Random fields on graphs
- 2.1.3 Specifications and their corresponding Gibbs states
- 2.1.4 Dobrushin-Pechersky conditions
- 2.2 Reconstruction procedure
- 2.2.1 Reconstruction in the case =2
- 2.2.2 Reconstruction in the case of 3
- 2.2.3 Reconstruction over a finite volume
- 2.3 Decay of correlations
- 2.4 Bibliographical notes
- Appendix 2.A The total variation distance
- Appendix 2.B Existence of tempered Gibbs measures
- 3 Classical lattice systems
- 3.1 Short description of the model
- 3.2 High-temperature uniqueness: 1
- 3.3 Low-temperature uniqueness: 1
- 4 Particle Systems in Continuum
- 4.1 Configuration spaces
- 4.1.1 Spaces of finite configurations
- 4.1.2 The configuration space
- 4.1.3 The Poisson and Lebesgue-Poisson measures
- 4.2 The case of pair interaction
- 4.2.1 Specifications and associated Gibbs measures
- 4.2.2 Conditions on the interaction
- 4.2.3 The associated lattice model
- 4.2.4 The uniqueness result
- 4.3 Systems with strong superstable interaction
- 4.4 The Lebowitz-Mazel-Presutti model
- 5 Gibbs States on Random Configurations: Annealed Approach
- 5.1 Description of the Model
- 5.2 Gibbsian formalism
- 5.3 Existence of Gibbs Measures
- 5.4 Uniqueness of Gibbs Measures
- 6 Equilibrium States on the Cone of Discrete Measures
- 6.1 Description of the model
- 6.2 Gibbsian formalism
- 6.3 Spatially bounded Lévy intensity measure
- 6.3.1 Exponential moment estimate
- 6.3.2 Existence of Gibbs measures
- 6.3.3 Uniqueness of Gibbs measures
- 6.4 Unbounded Lévy intensity measure
- Bibliography