| Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente Prochaine révisionLes deux révisions suivantes |
| mega:start [2017/05/04 13:11] – [Exposés à venir] male | mega:start [2017/05/26 02:19] – [Exposés à venir] male |
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| * Exposés de l'après-midi : [[http://www.normalesup.org/~dumaz/|Laure Dumaz]] [[dumaz@ceremade.dauphine.fr]] et [[http://camillemale.com|Camille Male]] [[camille.male@math.u-bordeaux.fr]] | * Exposés de l'après-midi : [[http://www.normalesup.org/~dumaz/|Laure Dumaz]] [[dumaz@ceremade.dauphine.fr]] et [[http://camillemale.com|Camille Male]] [[camille.male@math.u-bordeaux.fr]] |
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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. | |
| * 15h45-17h00: **[[http://pub.ist.ac.at/~jalt/|Johannes Alt]]** \\ // 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. | |
| * 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 | |
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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 |
| * 14h30-15h45: **[[https://people.kth.se/~schnelli/|Kevin Schnelli]]** | * 14h30-15h45: **[[https://people.kth.se/~schnelli/|Kevin Schnelli]]** // Free addition of random matrices and the local single ring theorem\\ //In the first part of this talk, I will discuss some recent results on local laws and rigidity of eigenvalues for additive random matrix models. In the second part, I will explain how these results can be used to derive the optimal convergence rate of the empirical eigenvalue distribution in the Single Ring Theorem. |
| * 15h45-17h00: | * 15h45-17h00: **[[http://www.isical.ac.in/~abose/|Arup Bose]]** //Large sample behaviour of high dimensional autocovariance matrices with application\\ //Consider a sample of size n from a linear process of dimension p where n, p grow to infinity and p/n converges. The existence of limiting spectral distribution (LSD) of symmetrized sum any sample autocovariance is known in the literature under appropriate (strong) assumptions on the coefficient matrices. Under significantly weaker conditions, we prove, in a unified way, that the LSD of any symmetric polynomial in these matrices exist. Our approach is through the more intuitive algebraic method of free probability that is applicable after an appropriate embedding, in conjunction with the method of moments. Thus, we are able to provide a general description for the limits in terms of some freely independent variables. All the previous results follow as special cases. We suggest statistical uses of these LSD and related results in problems such as order determination and white noise testing. |
| * 10h30-12h00: **[[http://www.normalesup.org/~decastro/|Yohann de Castro]]** | * 10h30-12h00: **[[http://www.normalesup.org/~decastro/|Yohann de Castro]]** // Quelques aspects statistiques de l'optimisation convexe en matrices aléatoires \\ //La minimisation convexe est une méthode très efficace en Statistique pour résoudre des systèmes d'équations linéaires où le nombre d'équations est bien plus petit que le nombre de variables. Pour que ce problème est un sens (et en vue des applications) on suppose que le nombre de variables non nulles à retrouver est contrôler. Dans ce cas, on sait résoudre exactement de tels systèmes d'équations linéaires dès lors que le noyau de la matrice du système vérifie une certaine propriété. J'expliquerai cette analyse dans un premier temps. Puis j'exposerai, la résolution d'un problème du même goût où l'on rajoute une perturbation et/ou on ne suppose plus de contrôle sur le nombre de variables non nulles à retrouver. |
| ===== Année 2016-2017 ===== | ===== Année 2016-2017 ===== |
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| * 15h45-17h00: **[[https://www.math.univ-toulouse.fr/~rchhaibi/|Reda Chhaibi]]** \\ //Maxima of characteristic polynomials and multiplicative chaos:// | * 15h45-17h00: **[[https://www.math.univ-toulouse.fr/~rchhaibi/|Reda Chhaibi]]** \\ //Maxima of characteristic polynomials and multiplicative chaos:// |
| * 10h30-12h00: **[[http://math.univ-lyon1.fr/~aubrun/|Guillaume Aubrun]]** \\ // Etats quantiques aléatoires: // | * 10h30-12h00: **[[http://math.univ-lyon1.fr/~aubrun/|Guillaume Aubrun]]** \\ // Etats quantiques aléatoires: // |
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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: // |
| | * 15h45-17h00: **[[http://pub.ist.ac.at/~jalt/|Johannes Alt]]** \\ // Local inhomogeneous circular law: // |
| | * 10h30-12h00: **[[http://pub.ist.ac.at/~lerdos/|Laszlo Erdös]]** \\ // The matrix Dyson equation in random matrix theory: // |
| ===== Année 2015-2016 ===== | ===== Année 2015-2016 ===== |
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