Higher order concentration for functions of weakly dependent random variables

Götze F, Sambale H, Sinulis A (2019)
Electronic Journal of Probability 24: 85.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
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.
Stichworte
concentration of measure; logarithmic Sobolev inequalities; Ising model
Erscheinungsjahr
2019
Zeitschriftentitel
Electronic Journal of Probability
Band
24
Art.-Nr.
85
ISSN
1083-6489
Page URI
https://pub.uni-bielefeld.de/record/2937741

Zitieren

Götze F, Sambale H, Sinulis A. Higher order concentration for functions of weakly dependent random variables. Electronic Journal of Probability. 2019;24: 85.
Götze, F., Sambale, H., & Sinulis, A. (2019). Higher order concentration for functions of weakly dependent random variables. Electronic Journal of Probability, 24, 85. doi:10.1214/19-EJP338
Götze, F., Sambale, H., and Sinulis, A. (2019). Higher order concentration for functions of weakly dependent random variables. Electronic Journal of Probability 24:85.
Götze, F., Sambale, H., & Sinulis, A., 2019. Higher order concentration for functions of weakly dependent random variables. Electronic Journal of Probability, 24: 85.
F. Götze, H. Sambale, and A. Sinulis, “Higher order concentration for functions of weakly dependent random variables”, Electronic Journal of Probability, vol. 24, 2019, : 85.
Götze, F., Sambale, H., Sinulis, A.: Higher order concentration for functions of weakly dependent random variables. Electronic Journal of Probability. 24, : 85 (2019).
Götze, Friedrich, Sambale, Holger, and Sinulis, Arthur. “Higher order concentration for functions of weakly dependent random variables”. Electronic Journal of Probability 24 (2019): 85.