The structure of low-complexity Gibbs measures on product spaces
From MaRDI portal
Publication:2189463
DOI10.1214/19-AOP1352zbMath1444.60006arXiv1810.07278MaRDI QIDQ2189463
Publication date: 15 June 2020
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1810.07278
Gibbs measuresnonlinear large deviationsdual total correlationgradient complexitymixtures of product measures
Probability measures on topological spaces (60B05) Stochastic processes (60G99) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Measures of information, entropy (94A17) Optimal transportation (49Q22)
Related Items
Upper tails via high moments and entropic stability, Taming correlations through entropy-efficient measure decompositions with applications to mean-field approximation, Replica symmetry in upper tails of mean-field hypergraphs, Upper tail of the spectral radius of sparse Erdös-Rényi graphs, Upper tail for homomorphism counts in constrained sparse random graphs, Nonlinear large deviations: beyond the hypercube, Upper Tail Large Deviations of Regular Subgraph Counts in Erdős‐Rényi Graphs in the Full Localized Regime, Large deviations of subgraph counts for sparse Erdős-Rényi graphs, A Dimension-Free Reverse Logarithmic Sobolev Inequality for Low-Complexity Functions in Gaussian Space, Multi-variate correlation and mixtures of product measures, Nonlinear large deviation bounds with applications to Wigner matrices and sparse Erdős-Rényi graphs, A transportation approach to the mean-field approximation, Spectral edge in sparse random graphs: upper and lower tail large deviations, Large deviations for the largest eigenvalue of Gaussian networks with constant average degree
Cites Work
- Unnamed Item
- Unnamed Item
- Probability in Banach spaces. Isoperimetry and processes
- I-divergence geometry of probability distributions and minimization problems
- Information inequalities and concentration of measure
- Measure concentration for a class of random processes
- Gaussian-width gradient complexity, reverse log-Sobolev inequalities and nonlinear large deviations
- Exponential random graphs behave like mixtures of stochastic block models
- Measure concentration and the weak Pinsker property
- Decomposition of mean-field Gibbs distributions into product measures
- Concentration of measure inequalities for Markov chains and \(\Phi\)-mixing processes.
- Concentration of measure and isoperimetric inequalities in product spaces
- Transportation cost for Gaussian and other product measures
- Large deviations for random graphs. École d'Été de Probabilités de Saint-Flour XLV -- 2015
- Upper tails and independence polynomials in random graphs
- Bounding \(\bar d\)-distance by informational divergence: A method to prove measure concentration
- Nonlinear large deviations
- A simple proof of the blowing-up lemma (Corresp.)
- Linear dependence structure of the entropy space
- Nonnegative entropy measures of multivariate symmetric correlations
- Real Analysis and Probability
- Elements of Information Theory
- On the variational problem for upper tails in sparse random graphs
