We prove a reverse form of the multidimensional Brascamp-Lieb inequality. Our method also gives a new way to derive the Brascamp-Lieb inequality and is rather convenient for the study of equality… (More)

It is shown that if X1, X2, . . . are independent and identically distributed square-integrable random variables then the entropy of the normalized sum Ent ( X1 + · · ·+ Xn √ n ) is an increasing… (More)

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general F -Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide… (More)

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 establish… (More)

It is shown that if X is a random variable whose density satisfies a Poincaré inequality, and Y is an independent copy of X, then the entropy of (X + Y )/ √ 2 is greater than that of X by a fixed… (More)

We give a new proof of the sharp form of Young’s inequality for convolutions, first proved by Beckner [Be] and Brascamp-Lieb [BL]. The latter also proved a sharp reverse inequality in the case of… (More)

R f log f , provided the positive part of the integral is finite. So Ent(X) ∈ [−∞, +∞). If X has variance 1, it is a classical fact that its entropy is well defined and bounded above by that of a… (More)

We study the isoperimetric problem for product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate half-spaces are… (More)

Adapting Borell’s proof of Ehrhard’s inequality for general sets, we provide a semi-group approach to the reverse Brascamp-Lieb inequality, in its “convexity” version.

We analyze combinatorial optimization problems over a random pair of points (X ,Y) in R of equal cardinal. Typical examples include the matching of minimal length, the traveling salesperson tour… (More)