Hypercontractivity and Comparison of Moments of Iterated Maxima and Minima of Independent Random Variables
Pawel Hitczenko, North Carolina State University
Stanislaw Kwapien, Warsaw University
Wenbo V. Li, University of Delaware
Gideon Schechtman, The Weizmann Institute of Science
Thomas Schlumprecht, Texas A&M University
Joel Zinn, Texas A&M University
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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