Colloque Functional inequalities

July 7th, 2016, Université Université Paris Nanterre

a scientific event organized by Nathaël Gozlan (LAMA), Cyril Roberto (Modal'X), Yan Shu (Modal'X)

Contact: natael.gozlan@u-pem.fr, cyril.roberto@math.cnrs.fr, yshu@parisnanterre.fr
 

Speakers

Ivan GENTIL, Université Claude Bernard Lyon 1

Mokshay MADIMAN, University of Delaware

Yan SHU, Université Université Paris Nanterre

Programme

09:45 - 10:15 Welcome

10:15 - 11:00 Lecture: Nouveaux développements autour de l'inégalité de Borell-Brascamp-Lieb, Ivan Gentil

Je vais revisiter les liens entre l'inégalité de Borell-Brascamp-Lieb et les inégalités de Sobolev et Gagliardo-Nirenberg à l'aide des équations de Hamilton-Jacobi.

11:15 - 12:00 Lecture: Entropy power inequalities in cyclic groups, and connections to additive combinatorics, Mokshay Madiman

While the Shannon-Stam entropy power inequality is a powerful tool in the study of convolutions of probability densities on \mathbb{R}^n, the search for a satisfactory discrete analogue of the same that is sharp has long been largely fruitless, with only some rather specialized results available. We prove several simple and sharp new lower bounds for the Rényi entropies of the convolution of probability distributions on the integers in terms of certain (discrete) rearrangements of these distributions. These inequalities may be thought of as discrete entropy power inequalities for integer-valued random variables. Furthermore, they provide a unification of the Cauchy-Davenport theorem on the integers from additive combinatorics, as well as of an influential lemma due to Littlewood-Offord and Erdos (which it significantly generalizes). If time permits, we will discuss extensions to cyclic groups of prime order.
The talk is based on joint work with Liyao Wang (J. P. Morgan) and Jae Oh Woo (University of Texas, Austin).

14:00 - 15:00 Thesis defense: Inf-convolution operators and weak transport inequalities in discrete spaces, Yan Shu

In this thesis, I study a variety of inf-convolution operators and their applications to a class of general transportation inequalities, more specifically in the graphs. We prove that some inf-convolution operators are solutions of a Hamilton-Jacobi’s inequation. We deduce from this result some properties concerning different functional inequalities, including Log-Sobolev inequalities and weak-transport inequalities.

Jury:
Frank BARTHE, Examinateur
Ivan GENTIL, Rapporteur
Nathaël GOZLAN, Directeur de thèse
Christian LEONARD, Examinateur
Mokshay MADIMAN, Rapporteur
Cyril ROBERTO, Directeur de thèse

16:00 Pot

 

Registration

 

Practical information

Venue:

Morning: salle E06 (entresol, bât. G)
Afternoon: salle G614 (6th floor, bât. G)

Modal'X, Université Université Paris Nanterre
200 av. de la République, 92001 Nanterre

instructions

Transportation: RER A or Transilien L, station Université Paris Nanterreniversité