On concentration inequalities and their applications for Gibbs measures in lattice systems

DOI10.1007/s10955-017-1884-xzbMath1382.82008arXiv1610.06502OpenAlexW2532628754MaRDI QIDQ1691507

Jean Rene Chazottes, Pierre Collet, Frank Redig

Publication date: 16 January 2018

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

Full work available at URL: https://arxiv.org/abs/1610.06502

zbMATH Keywords

relative entropyempirical measure\(\bar{d}\)-distanceKantorovich distanceDobrushin uniquenessalmost-sure central limit theoremGaussian concentration boundlow-temperature Ising modelmoment concentration bound

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (6)

A note on concentration for polynomials in the Ising model ⋮ Gaussian concentration and uniqueness of equilibrium states in lattice systems ⋮ Gaussian concentration bound and ensemble equivalence in generic quantum many-body systems including long-range interactions ⋮ Gaussian concentration bound for potentials satisfying Walters condition with subexponential continuity rates ⋮ Evolution of concentration under lattice spin-flip dynamics ⋮ Modified log-Sobolev inequalities, Beckner inequalities and moment estimates

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