Open Access
2019 A note on concentration for polynomials in the Ising model
Radosław Adamczak, Michał Kotowski, Bartłomiej Polaczyk, Michał Strzelecki
Electron. J. Probab. 24: 1-22 (2019). DOI: 10.1214/19-EJP280


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.


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Radosław Adamczak. Michał Kotowski. Bartłomiej Polaczyk. Michał Strzelecki. "A note on concentration for polynomials in the Ising model." Electron. J. Probab. 24 1 - 22, 2019.


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

zbMATH: 07055680
MathSciNet: MR3949267
Digital Object Identifier: 10.1214/19-EJP280

Primary: 60E15 , 82B99

Keywords: concentration of measure , Ising model , polynomials , Transportation inequalities

Vol.24 • 2019
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