Decomposition of mean-field Gibbs distributions into product measures

DOI10.1214/18-EJP159zbMath1390.60346arXiv1708.05859OpenAlexW2963169888MaRDI QIDQ1748940

Renan Gross, Ronen Eldan

Publication date: 15 May 2018

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.05859

zbMATH Keywords

large deviationIsing modelGibbs distributionmean fieldsparse random graphsGaussian width

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Large deviations (60F10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (13)

Gaussian-width gradient complexity, reverse log-Sobolev inequalities and nonlinear large deviations ⋮ Exponential random graphs behave like mixtures of stochastic block models ⋮ Dimension reduction in vertex-weighted exponential random graphs ⋮ Upper tails via high moments and entropic stability ⋮ Taming correlations through entropy-efficient measure decompositions with applications to mean-field approximation ⋮ The structure of low-complexity Gibbs measures on product spaces ⋮ Joint estimation of parameters in Ising model ⋮ Large deviations of subgraph counts for sparse Erdős-Rényi graphs ⋮ Multi-variate correlation and mixtures of product measures ⋮ Decomposition of mean-field Gibbs distributions into product measures ⋮ A transportation approach to the mean-field approximation ⋮ Approximating stationary distributions of fast mixing Glauber dynamics, with applications to exponential random graphs ⋮ Preferential attachment when stable

Cites Work

• Skorokhod embeddings via stochastic flows on the space of Gaussian measures
• Decomposition of mean-field Gibbs distributions into product measures
• Universality of the mean-field for the Potts model
• Estimating and understanding exponential random graph models
• Nonlinear large deviations
• Extreme Points of Moment Sets
• Analysis of Boolean Functions
• On the variational problem for upper tails in sparse random graphs

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