| Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente Prochaine révisionLes deux révisions suivantes |
| mega:start [2017/03/30 10:40] – [Exposés à venir] male | mega:start [2017/04/20 11:57] – [Exposés à venir] male |
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| | * Vendredi **5 Mai 2017**, Amphi Hermite le matin, salle 314 l'après midi |
| | * 14h30-15h45: **[[https://ion.nechita.net/about/|Ion Nechita]]** \\ // Block-modified random matrices and applications to entanglement theory: // Motivated by the problem of entanglement detection in quantum information theory, we study the spectrum of random matrices which have been modified by a linear map acting on their blocks. More precisely, for a unitarily invariant random matrix acting on a tensor product space, we consider the matrix obtained by acting with a fixed, hermiticity preserving map, on one factor of the tensor product. We discuss the limiting spectral distribution of the modified matrix, in terms of the initial distribution of the random matrix, and of the linear map acting on the blocks. The key ingredient in the proof is a freeness result, with amalgamation over a commutative and finite dimensional algebra related to the linear map. The talk is based on http://arxiv.org/abs/1508.05732 and on some work in progress. |
| * Vendredi **14 Avril 2017**, salle 314 | * 15h45-17h00: **[[https://sites.google.com/site/torbenkruegermath/|Torben Krüger]]** \\ // Local inhomogeneous circular law: // We consider large random matrices X with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical variances, the limiting density is uniform. In this special case, the local circular law by Bourgade et. al. shows that the empirical density converges even locally on scales slightly above the typical eigenvalue spacing. In the general case, the limiting density is typically inhomogeneous and it is obtained via solving a system of deterministic equations. Our main result is the local inhomogeneous circular law in the bulk spectrum on the optimal scale for a general variance profile of the entries of X. It is a joint work with Johannes Alt and Laszlo Erdos, IST Austria. |
| * 14h30-15h45: **[[https://www.math.u-psud.fr/~meliot/|Pierre-Loïc Méliot]]** \\ //Spectre d’un graphe aléatoire géométrique sur un groupe de Lie compact:// Soit G un groupe de Lie compact, par exemple G=SU(3), et L un réel positif. On considère le graphe aléatoire obtenu en prenant dans le groupe N points indépendants suivant la mesure de Haar, et en reliant deux de ces points s’ils sont à distance géodésique inférieure à L. On s’intéresse alors au spectre de la matrice d’adjacence A(N,L) du graphe. 1. Si L est fixé et N tend vers l’infini (régime gaussien), alors les plus grandes valeurs propres ont une asymptotique décrite par certaines combinaisons de fonctions de Bessel. En particulier, on peut facilement estimer le rayon spectral et le trou spectral. 2. Si N tend vers l’infini et L=L(N)=O(N^{-1/dim G}) (régime poissonien), alors la mesure spectrale de A(N,L(N)) a une limite non triviale. Le calcul des moments de cette limite repose sur une étude asymptotique des représentations de G, où la formule de Weyl dégénère en une dérivée partielle, et où les produits tensoriels de représentations dégénèrent en des mesures supportées par des polyèdres. | * 10h30-12h00: **[[http://pub.ist.ac.at/~lerdos/|Laszlo Erdös]]** \\ // The matrix Dyson equation in random matrix theory: // The asymptotic density of states for Wigner matrices is computed by solving a simple quadratic scalar equation for its Stieltjes transform. For random matrices with correlated entries, the corresponding equation becomes a self-consistent matrix equation. We present a comprehensive analysis of this matrix Dyson equation which, in particular, leads to the Wigner-Dyson-Mehta spectral universality for large random matrices with a decaying but otherwise general correlation structure. It is a joint work with Oskari Ajanki and Torben Kruger, IST Austria |
| * 15h45-17h00: **[[https://www.math.univ-toulouse.fr/~rchhaibi/|Reda Chhaibi]]** \\ //Maxima of characteristic polynomials and multiplicative chaos:// I want to explain why characteristic polynomials of (finite) random matrices behave like log-correlated Gaussian fields. More precisely, they form a peculiar regularization of the so-called Gaussian Multiplicative Chaos, introduced by JP Kahane. The analogy leads to many conjectures on the fractal measure defined by absolute continuity with respect to the Lebesgue measure, or simply the global maxima. Among the rigorous results, I will report on a recent work in collaboration with J. Najnudel and T. Madaule (arxiv 1607.00243), where we made progress in understanding the extremal values of (the logarithm of) the characteristic polynomial of a random unitary matrix whose spectrum is distributed according the Circular Beta Ensemble (CβE). | |
| * 10h30-12h00: **[[http://math.univ-lyon1.fr/~aubrun/|Guillaume Aubrun]]** | |
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| * Vendredi **5 Mai 2017**, salle 421 le matin, salle 314 l'après midi | |
| * 14h30-15h45: | |
| * 15h45-17h00: **[[https://sites.google.com/site/torbenkruegermath/|Torben Krüger]]** | |
| * 10h30-12h00: **[[http://pub.ist.ac.at/~lerdos/|Laszlo Erdös]]** | |
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| * Vendredi **2 Juin 2017**, salle 421 le matin, salle 314 l'après midi | * Vendredi **2 Juin 2017**, salle 421 le matin, salle 314 l'après midi |