Concentration inequalities for polynomials in alpha-sub-exponential random variables

Götze F, Sambale H, Sinulis A (2021)
Electronic Journal of Probability 26: 48.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We derive multi-level concentration inequalities for polynomials in independent random variables with an alpha-sub-exponential tail decay. A particularly interesting case is given by quadratic forms f (X-1, ..., X-n) = < X, AX >, for which we prove Hanson-Wright-type inequalities with explicit dependence on various norms of the matrix A. A consequence of these inequalities is a two-level concentration inequality for quadratic forms in alpha-sub-exponential random variables, such as quadratic Poisson chaos. We provide various applications of these inequalities. Among them are generalizations of some results proven by Rudelson and Vershynin from sub-Gaussian to alpha-sub-exponential random variables, i. e. concentration of the Euclidean norm of the linear image of a random vector and concentration inequalities for the distance between a random vector and a fixed subspace.
Stichworte
concentration of measure phenomenon; Orlicz norms; Hanson-Wright; inequality; Poisson chaos; sub-exponential random variables
Erscheinungsjahr
2021
Zeitschriftentitel
Electronic Journal of Probability
Band
26
Art.-Nr.
48
eISSN
1083-6489
Page URI
https://pub.uni-bielefeld.de/record/2955131

Zitieren

Götze F, Sambale H, Sinulis A. Concentration inequalities for polynomials in alpha-sub-exponential random variables. Electronic Journal of Probability. 2021;26: 48.
Götze, F., Sambale, H., & Sinulis, A. (2021). Concentration inequalities for polynomials in alpha-sub-exponential random variables. Electronic Journal of Probability, 26, 48. https://doi.org/10.1214/21-EJP606
Götze, F., Sambale, H., and Sinulis, A. (2021). Concentration inequalities for polynomials in alpha-sub-exponential random variables. Electronic Journal of Probability 26:48.
Götze, F., Sambale, H., & Sinulis, A., 2021. Concentration inequalities for polynomials in alpha-sub-exponential random variables. Electronic Journal of Probability, 26: 48.
F. Götze, H. Sambale, and A. Sinulis, “Concentration inequalities for polynomials in alpha-sub-exponential random variables”, Electronic Journal of Probability, vol. 26, 2021, : 48.
Götze, F., Sambale, H., Sinulis, A.: Concentration inequalities for polynomials in alpha-sub-exponential random variables. Electronic Journal of Probability. 26, : 48 (2021).
Götze, Friedrich, Sambale, Holger, and Sinulis, Arthur. “Concentration inequalities for polynomials in alpha-sub-exponential random variables”. Electronic Journal of Probability 26 (2021): 48.

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