Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables

Details Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables

1996-07-18

arxiv.org/abs/math/9607209v1

Mathematics

Probability

Scientific paper

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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