Electronic Journal of Probability

Hypercontractivity and Comparison of Moments of Iterated Maxima and Minima of Independent Random Variables

Pawel Hitczenko, Stanislaw Kwapien, Wenbo Li, Gideon Schechtman, Thomas Schlumprecht, and Joel Zinn

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Abstract

We provide necessary and sufficient conditions for hypercontractivity of the minima of nonnegative, i.i.d. random variables and of both the maxima of minima and the minima of maxima for such r.v.'s. It turns out that the idea of hypercontractivity for minima is closely related to small ball probabilities and Gaussian correlation inequalities.

Article information

Source
Electron. J. Probab., Volume 3 (1998), paper no. 2, 26 pp.

Dates
Accepted: 7 January 1998
First available in Project Euclid: 29 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1454101762

Digital Object Identifier
doi:10.1214/EJP.v3-24

Mathematical Reviews number (MathSciNet)
MR1491527

Zentralblatt MATH identifier
0889.60003

Subjects
Primary: 60B11: Probability theory on linear topological spaces [See also 28C20] 60E07: Infinitely divisible distributions; stable distributions 60E15: Inequalities; stochastic orderings
Secondary: 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx] 60G15: Gaussian processes

Keywords
hypercontractivity comparison of moments iterated maxima and minima Gaussian correlation inequalities small ball probabilities

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Hitczenko, Pawel; Kwapien, Stanislaw; Li, Wenbo; Schechtman, Gideon; Schlumprecht, Thomas; Zinn, Joel. Hypercontractivity and Comparison of Moments of Iterated Maxima and Minima of Independent Random Variables. Electron. J. Probab. 3 (1998), paper no. 2, 26 pp. doi:10.1214/EJP.v3-24. https://projecteuclid.org/euclid.ejp/1454101762


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