7 citations · 11 across the 3 of their papers we have counts for
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math.PR2005★ 7 cited
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…
math.PR2004★ 2 cited
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…
math.PR2003★ 2 cited
A criterion for Talagrand's quadratic transportation cost inequality
Patrick Cattiaux, Arnaud Guillin
We show that the quadratic transportation cost inequality is equivalent to both a Poincaré inequality and a strong form of the Gaussian concentration property. The main ingre…