Concentration inequalities for polynomials of contracting Ising models

DOI10.1214/18-ECP173zbMath1405.82009arXiv1706.00121OpenAlexW2963245826MaRDI QIDQ1990045

Eyal Lubetzky, Reza Gheissari, Yuval Peres

Publication date: 24 October 2018

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

Full work available at URL: https://arxiv.org/abs/1706.00121

zbMATH Keywords

contractionIsing modelconcentration of measureindependence testing

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (10)

A note on concentration for polynomials in the Ising model ⋮ Concentration of Markov chains indexed by trees ⋮ Long-term concentration of measure and cut-off ⋮ Fluctuations in mean-field Ising models ⋮ Higher order concentration for functions of weakly dependent random variables ⋮ Approximating stationary distributions of fast mixing Glauber dynamics, with applications to exponential random graphs ⋮ Stein's method for stationary distributions of Markov chains and application to Ising models ⋮ Modified log-Sobolev inequalities, Beckner inequalities and moment estimates ⋮ On testing for parameters in Ising models ⋮ Property testing in high-dimensional Ising models

Cites Work

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• Concentration inequalities for random fields via coupling
• Concentration inequalities for functions of Gibbs fields with application to diffraction and random Gibbs measures
• Concentration of measure inequalities for Markov chains and \(\Phi\)-mixing processes.
• A measure concentration inequality for contracting Markov chains
• Concentration inequalities for dependent random variables via the martingale method
• Concentration of measure and mixing for Markov chains
• Measure concentration and strong mixing
• Testing Ising Models
• Analytic Extensions of Differentiable Functions Defined in Closed Sets

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