Correlation inequalities and monotonicity properties of the Ruelle operator

DOI10.1142/S0219493719500485zbMath1453.37028arXiv1703.06126MaRDI QIDQ5213061

Artur Oscar Lopes, Leandro M. Cioletti

Publication date: 31 January 2020

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.06126

zbMATH Keywords

thermodynamic formalismRuelle operatorFKG inequality

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (6)

On information gain, Kullback-Leibler divergence, entropy production and the involution kernel ⋮ Interactions, specifications, DLR probabilities and the Ruelle operator in the one-dimensional lattice ⋮ Gibbs states and Gibbsian specifications on the space ℝ^ℕ ⋮ Existence of Gibbs states and maximizing measures on a general one-dimensional lattice system with Markovian structure ⋮ Nonequilibrium in thermodynamic formalism: the second law, gases and information geometry ⋮ The involution kernel and the dual potential for functions in the Walters' family

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gibbs measures and phase transitions.
• Interacting particle systems. With a new postface.
• Entropy, large deviations, and statistical mechanics.
• Correlation inequalities on some partially ordered sets
• Nonuniqueness in \(g\)-functions
• Entropic repulsion and lack of the \(g\)-measure property for Dyson models
• Ruelle operator for continuous potentials and DLR-Gibbs measures
• Existence of a phase-transition in a one-dimensional Ising ferromagnet
• Interactions, specifications, DLR probabilities and the Ruelle operator in the one-dimensional lattice
• Decimation of the Dyson-Ising ferromagnet
• Phase transitions in one-dimensional translation invariant systems: a Ruelle operator approach
• Duality between eigenfunctions and eigendistributions of Ruelle and Koopman operators via an integral kernel
• Entropy and variational principle for one-dimensional lattice systems with a generala prioriprobability: positive and zero temperature
• Uniqueness and ergodic properties of attractive g-measures
• Examples for the Nonuniqueness of the Equilibrium State
• An example of non-unique g -measures
• Spectral properties of the Ruelle operator for product-type potentials on shift spaces
• A LARGE DEVIATION PRINCIPLE FOR THE EQUILIBRIUM STATES OF HÖLDER POTENTIALS: THE ZERO TEMPERATURE CASE
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Phase transitions in long-range Ising models and an optimal condition for factors of -measures

This page was built for publication: Correlation inequalities and monotonicity properties of the Ruelle operator