Concentration inequalities for functions of Gibbs fields with application to diffraction and random Gibbs measures

DOI10.1007/s00220-003-0841-5zbMath1023.60080OpenAlexW2060534685MaRDI QIDQ1404743

Christof Külske

Publication date: 21 August 2003

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-003-0841-5

zbMATH Keywords

concentration inequalitiesrandom Gibbs measureGibbs fieldDobrushin uniquenessDobrushin constant

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44)

Related Items (18)

Continuity of eigenfunctions of uniquely ergodic dynamical systems and intensity of Bragg peaks ⋮ Concentration inequalities for random fields via coupling ⋮ Quantum concentration inequalities ⋮ Gaussian concentration and uniqueness of equilibrium states in lattice systems ⋮ On concentration inequalities and their applications for Gibbs measures in lattice systems ⋮ Gaussian concentration bounds for stochastic chains of unbounded memory ⋮ Gaussian concentration bound and ensemble equivalence in generic quantum many-body systems including long-range interactions ⋮ The Poincaré inequality for Markov random fields proved via disagreement percolation ⋮ Comparison theorems for Gibbs measures ⋮ Concentration inequalities for polynomials of contracting Ising models ⋮ Random fields on model sets with localized dependency and their diffraction ⋮ Absence of singular continuous diffraction for discrete multi-component particle models ⋮ Close-packed dimers on the line: diffraction versus dynamical spectrum ⋮ Diffraction of stochastic point sets: Explicitly computable examples ⋮ Higher order concentration for functions of weakly dependent random variables ⋮ Coupling, concentration inequalities, and stochastic dynamics ⋮ Evolution of concentration under lattice spin-flip dynamics ⋮ On limit theorems for persistent Betti numbers from dependent data

Cites Work

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• A new look at independence
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• Spectral theory and x-ray diffraction
• Diffractive point sets with entropy
• Weighted Dirac combs with pure point diffraction
• Diffraction by aperiodic structures at high temperatures
• Weakly Gibbsian representations for joint measures of quenched lattice spin models.
• Large deviation principles for Euclidean functionals and other nearly additive processes
• Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields

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