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The circular law
The circular law theorem states that the empirical spectral distribution of a n×n random matrix with i.i.d. entries of variance 1/n tends to the uniform law on the unit disc of the complex plane asExpand
Around the circular law
These expository notes are centered around the circular law theorem, which states that the empirical spectral distribution of a nxn random matrix with i.i.d. entries of variance 1/n tends to theExpand
Sur les in'egalit'es de Sobolev logarithmiques
On logarithmic Sobolev inequalities). — This book is an overview on logarithmic Sobolev inequalities. These inequalities turned out to be a subject of intense activity during the past years, fromExpand
Interactions between compressed sensing, random matrices, and high dimensional geometry
Short courses given at the occasion of a school held in Universite Paris-Est Marne-la-Vallee, 16–20 November 2009, by Djalil Chafai, Olivier Guedon, Guillaume Lecue, Alain Pajor, and Shahar Mendelson are expanded. Expand
Channel selection methods for infrared atmospheric sounding interferometer radiances
Advanced infrared sounders will provide thousands of radiance data at every observation location. The number of individual pieces of information is not usable in an operational numericalExpand
This article provides entropic inequalities for binomial-Poisson distributions, derived from the two point space. They appear as local inequalities of the M/M/∞ queue. They describe in particular theExpand
Entropies, convexity, and functional inequalities : On Phi-entropies and Phi-Sobolev inequalities
Our aim is to provide a short and self contained synthesis which generalise and unify various related and unrelated works involving what we call Phi-Sobolev functional inequalities. Such inequalitiesExpand
First order global asymptotics for confined particles with singular pair repulsion
We study a physical system of N interacting particles in Rd, subject to pair repulsion and confined by an external field. We establish a large deviations principle for their empirical distribution asExpand
Circular law theorem for random Markov matrices
Let (Xjk)jk≥1 be i.i.d. nonnegative random variables with bounded density, mean m, and finite positive variance σ2. Let M be the n × n random Markov matrix with i.i.d. rows defined byExpand
On gradient bounds for the heat kernel on the Heisenberg group
It is known that the couple formed by the two dimensional Brownian motion and its Levy area leads to the heat kernel on the Heisenberg group, which is one of the simplest sub-Riemannian space. TheExpand