Electronic Journal of Probability

Higher order concentration for functions of weakly dependent random variables

Friedrich Götze, Holger Sambale, and Arthur Sinulis

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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.

Article information

Electron. J. Probab., Volume 24 (2019), paper no. 85, 19 pp.

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

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Primary: 60E15: Inequalities; stochastic orderings

concentration of measure logarithmic Sobolev inequalities Ising model

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Götze, Friedrich; Sambale, Holger; Sinulis, Arthur. Higher order concentration for functions of weakly dependent random variables. Electron. J. Probab. 24 (2019), paper no. 85, 19 pp. doi:10.1214/19-EJP338. https://projecteuclid.org/euclid.ejp/1568080865

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