Gibbs measures and phase transitions on sparse random graphs

DOI10.1214/09-BJPS027zbMath1205.05209arXiv0910.5460OpenAlexW2963994072MaRDI QIDQ985984

Amir Dembo, Andrea Montanari

Publication date: 9 August 2010

Published in: Brazilian Journal of Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.5460

zbMATH Keywords

phase transitionsspin modelsrandom graphsIsing modelGibbs measuressparse graphslocal weak convergence

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Phase transitions (general) in equilibrium statistical mechanics (82B26) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items

Universality of the mean-field for the Potts model, Load balancing in hypergraphs, Ising critical behavior of inhomogeneous Curie-Weiss models and annealed random graphs, Finite size scaling functions of the phase transition in the ferromagnetic Ising model on random regular graphs, Information-theoretic thresholds from the cavity method, On the phase transition in random simplicial complexes, Critical value asymptotics for the contact process on random graphs, Maximum independent sets on random regular graphs, Glauber dynamics for Ising models on random regular graphs: cut-off and metastability, Ising models on power-law random graphs, Mean quantum percolation, Marginal dynamics of interacting diffusions on unimodular Galton-Watson trees, Matchings on trees and the adjacency matrix: A determinantal viewpoint, Solution of the monomer-dimer model on locally tree-like graphs. Rigorous results, Local weak convergence for sparse networks of interacting processes, Fluctuations in mean-field Ising models, Nonbacktracking Spectral Clustering of Nonuniform Hypergraphs, Interacting stochastic processes on sparse random graphs, Detecting structured signals in Ising models, Joint estimation of parameters in Ising model, Factor models on locally tree-like graphs, Zero-temperature dynamics in the dilute Curie-Weiss model, The replica symmetric solution for Potts models on \(d\)-regular graphs, Majority dynamics on trees and the dynamic cavity method, Ising critical exponents on random trees and graphs, Statistical Matching Theory, Survival and extinction of epidemics on random graphs with general degree, Mean-Field Monomer-Dimer Models. A Review, Bethe states of random factor graphs, Fluctuations of the magnetization in the \(p\)-spin Curie-Weiss model, Error bounds in local limit theorems using Stein's method, Unnamed Item, Gibbs measures over locally tree-like graphs and percolative entropy over infinite regular trees, A note on dynamical models on random graphs and Fokker-Planck equations, Large deviations for the annealed Ising model on inhomogeneous random graphs: spins and degrees, Fluctuations of the Magnetization for Ising models on Erd\H{o}s-R\'enyi Random Graphs -- the Regimes of Low Temperature and External Magnetic Field, The Hopfield model on a sparse Erdös-Renyi graph, Spin systems on Bethe lattices, Combinatorial approach to the interpolation method and scaling limits in sparse random graphs, The condensation phase transition in random graph coloring, The set of solutions of random XORSAT formulae, Examples in the entropy theory of countable group actions, Fluctuations for the partition function of Ising models on Erdös-Rényi random graphs, Annealed Ising model on configuration models, Phase growth with heat diffusion in a stochastic lattice model, Fluctuations of the magnetization for Ising models on dense Erdős-Rényi random graphs, Weighted enumeration of spanning subgraphs in locally tree-like graphs, Unnamed Item, On local weak limit and subgraph counts for sparse random graphs, Fluctuations of the magnetization for Ising models on Erdős–Rényi random graphs—the regimes of small p and the critical temperature ^*, A short survey on stable polynomials, orientations and matchings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Reconstruction of random colourings
• Reconstruction on trees and spin glass transition
• Rigorous inequalities between length and time scales in glassy systems
• Finite size scaling for the core of large random hypergraphs
• Ising models on locally tree-like graphs
• The high temperature region of the Viana-Bray diluted spin glass model
• On the hardness of sampling independent sets beyond the tree threshold
• A probabilistic proof of an asymptotic formula for the number of labelled regular graphs
• Gibbs measures and phase transitions
• Information flow on trees
• On the purity of the limiting Gibbs state for the Ising model on the Bethe lattice.
• Glauber dynamics on trees: Boundary conditions and mixing time
• Glauber dynamics on trees and hyperbolic graphs
• Broadcasting on trees and the Ising model.
• Sudden emergence of a giant \(k\)-core in a random graph
• Existence of a phase-transition in a one-dimensional Ising ferromagnet
• The Canophy graph and level statistics for random operators on trees
• Coloring Random Graphs
• Optimal phylogenetic reconstruction
• Network delay inference from additive metrics
• Reconstruction and Clustering in Random Constraint Satisfaction Problems
• Reconstruction for Colorings on Trees
• Modern Coding Theory
• Information, Physics, and Computation
• Percolation
• Sharp thresholds of graph properties, and the $k$-sat problem
• Séminaire de Probabilités XXXVI
• Mixing in time and space for lattice spin systems: A combinatorial view
• Gibbs states and the set of solutions of random constraint satisfaction problems
• On the solution-space geometry of random constraint satisfaction problems
• The two possible values of the chromatic number of a random graph