A note on concentration for polynomials in the Ising model

Abstract

We present precise multilevel exponential concentration inequalities for polynomials in Ising models satisfying the Dobrushin condition. The estimates have the same form as two-sided tail estimates for polynomials in Gaussian variables due to Latała. In particular, for quadratic forms we obtain a Hanson-Wright type inequality. We also prove concentration results for convex functions and estimates for nonnegative definite quadratic forms, analogous as for quadratic forms in i.i.d. Rademacher variables, for more general random vectors satisfying the approximate tensorization property for entropy.

References in corpus (7)

• Estimates of moments and tails of Gaussian chaoses
• Higher order concentration for functions of weakly dependent random variables
• Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails
• On the boundedness of Bernoulli processes
• On concentration inequalities and their applications for Gibbs measures in lattice systems
• On the convex Poincaré inequality and weak transportation inequalities
• A characterization of a class of convex log-Sobolev inequalities on the real line

Cited by in corpus (4)

• Logarithmic Sobolev inequalities for finite spin systems and applications
• Modified log-Sobolev inequalities, Beckner inequalities and moment estimates
• Concentration inequalities for bounded functionals via generalized log-Sobolev inequalities
• Modified log-Sobolev inequalities and two-level concentration