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1998 Hypercontractivity and Comparison of Moments of Iterated Maxima and Minima of Independent Random Variables
Pawel Hitczenko, Stanislaw Kwapien, Wenbo Li, Gideon Schechtman, Thomas Schlumprecht, Joel Zinn
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Electron. J. Probab. 3: 1-26 (1998). DOI: 10.1214/EJP.v3-24

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.

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Pawel Hitczenko. Stanislaw Kwapien. Wenbo Li. Gideon Schechtman. Thomas Schlumprecht. Joel Zinn. "Hypercontractivity and Comparison of Moments of Iterated Maxima and Minima of Independent Random Variables." Electron. J. Probab. 3 1 - 26, 1998. https://doi.org/10.1214/EJP.v3-24

Information

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

zbMATH: 0889.60003
MathSciNet: MR1491527
Digital Object Identifier: 10.1214/EJP.v3-24

Subjects:
Primary: 60B11 , 60E07 , 60E15
Secondary: 52A21 , 60G15

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

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Vol.3 • 1998
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