Gibbs measures over locally tree-like graphs and percolative entropy over infinite regular trees

DOI10.1007/s10955-018-1959-3zbMath1391.82005arXiv1705.03589OpenAlexW3100015600MaRDI QIDQ1753259

Moumanti Podder, Tim D. Austin

Publication date: 28 May 2018

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.03589

zbMATH Keywords

Ising modelPotts modelsofic entropyinfinite regular treelocally tree-like graphsstrong spatial mixingcolouring modelindependent set modelpercolative entropy

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Ergodicity, mixing, rates of mixing (37A25) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Convergence of probability measures (60B10) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items (6)

Entropy of quantum Markov states on Cayley trees ⋮ Limiting entropy of determinantal processes ⋮ Entropy and expansion ⋮ On structure of topological entropy for tree-shift of finite type ⋮ Predictability, topological entropy, and invariant random orders ⋮ The Lanford–Ruelle theorem for actions of sofic groups

Cites Work

• Unnamed Item
• Gibbs measures and phase transitions.
• The weak limit of Ising models on locally tree-like graphs
• Gibbs measures and phase transitions on sparse random graphs
• A generalized Shannon-McMillan theorem for the action of an amenable group on a probability space
• Glauber dynamics on trees and hyperbolic graphs
• Factor models on locally tree-like graphs
• The replica symmetric solution for Potts models on \(d\)-regular graphs
• The entropy of Gibbs measures on sofic groups
• Counting independent sets up to the tree threshold
• ADDITIVITY PROPERTIES OF SOFIC ENTROPY AND MEASURES ON MODEL SPACES
• Specific characteristics and variational principle for homogeneous random fields
• Counting without sampling: Asymptotics of the log-partition function for certain statistical physics models
• Thermodynamic Formalism
• Left and right convergence of graphs with bounded degree
• Strong spatial mixing of list coloring of graphs

This page was built for publication: Gibbs measures over locally tree-like graphs and percolative entropy over infinite regular trees