Electronic Journal of Probability

A note on concentration for polynomials in the Ising model

Radosław Adamczak, Michał Kotowski, Bartłomiej Polaczyk, and Michał Strzelecki

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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.

Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 42, 22 pp.

Dates
Received: 10 September 2018
Accepted: 17 February 2019
First available in Project Euclid: 17 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1555466612

Digital Object Identifier
doi:10.1214/19-EJP280

Mathematical Reviews number (MathSciNet)
MR3949267

Zentralblatt MATH identifier
07055680

Subjects
Primary: 60E15: Inequalities; stochastic orderings 82B99: None of the above, but in this section

Keywords
concentration of measure transportation inequalities Ising model polynomials

Rights
Creative Commons Attribution 4.0 International License.

Citation

Adamczak, Radosław; Kotowski, Michał; Polaczyk, Bartłomiej; Strzelecki, Michał. A note on concentration for polynomials in the Ising model. Electron. J. Probab. 24 (2019), paper no. 42, 22 pp. doi:10.1214/19-EJP280. https://projecteuclid.org/euclid.ejp/1555466612


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