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2019 Higher order concentration for functions of weakly dependent random variables
Friedrich Götze, Holger Sambale, Arthur Sinulis
Electron. J. Probab. 24: 1-19 (2019). DOI: 10.1214/19-EJP338

Abstract

We extend recent higher order concentration results in the discrete setting to include functions of possibly dependent variables whose distribution (on the product space) satisfies a logarithmic Sobolev inequality with respect to a difference operator that arises from Glauber type dynamics. Examples include the Ising model on a graph with $n$ sites with general, but weak interactions (i.e. in the Dobrushin uniqueness regime), for which we prove concentration results of homogeneous polynomials, as well as random permutations, and slices of the hypercube with dynamics given by either the Bernoulli-Laplace or the symmetric simple exclusion processes.

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Friedrich Götze. Holger Sambale. Arthur Sinulis. "Higher order concentration for functions of weakly dependent random variables." Electron. J. Probab. 24 1 - 19, 2019. https://doi.org/10.1214/19-EJP338

Information

Received: 9 May 2018; Accepted: 25 June 2019; Published: 2019
First available in Project Euclid: 10 September 2019

zbMATH: 07107392
MathSciNet: MR4003138
Digital Object Identifier: 10.1214/19-EJP338

Subjects:
Primary: 60E15

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