181 citations · 190 across the 3 of their papers we have counts for
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Concentration for independent random variables with heavy tails
Franck Barthe, Patrick Cattiaux, Cyril Roberto
If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we e…
A probabilistic approach to the geometry of the \ell_p^n-ball
Franck Barthe, Olivier Guedon, Shahar Mendelson +1
This article investigates, by probabilistic methods, various geometric questions on B_p^n, the unit ball of \ell_p^n. We propose realizations in terms of independent random variabl…
Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
F. Barthe, P. Cattiaux, C. Roberto
We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general -Sobolev inequalities, thus extending Gross hypercontractivity the…