| Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente Prochaine révisionLes deux révisions suivantes |
| mega:seminaire [2018/12/04 17:28] – Laure DUMAZ | mega:seminaire [2019/03/11 20:30] – [Prochaine séance] male |
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| {{ :mega:20141121_153039.jpg?400 |}} | {{ :mega:20141121_153039.jpg?400 |}} |
| ===== Prochaine séance ===== | ===== Prochaine séance ===== |
| * Vendredi **7 Décembre, salle 201** | * Vendredi **15 Mars** salle 421 |
| * 10h30-12h00: mini cours par **[[http://www.lpsm.paris/pageperso/lin/|Shen Lin]]** //Mesures harmoniques sur les frontières d'arbres aléatoires//\\ We will discuss some fractal properties of the harmonic measure on the infinite boundary of a supercritical Galton-Watson tree, which is defined as the law of loop-erased trajectory of a transient random walk on the tree. When the underlying tree becomes a critical Galton-Watson tree conditioned to have large height, we will also consider the exit distribution of a finite ball by simple random walk on the tree.\\ | * mini cours par **[[https://www.di.ens.fr/~lelarge/|Marc Lelarge]]** //The cavity method for the spiked Wigner model.// We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension setting for the mutual information between the signal and the observations, as well as the matrix minimum mean squared error, while the rank of the signal remains constant. We unify and generalize a number of recent works on PCA, sparse PCA, submatrix localization or community detection by computing the information-theoretic limits for these problems in the high noise regime. \\ |
| * 14h00-15h00: **[[https://www.math.toronto.edu/~marcin/|Marcin Kotowski]]** //Tracy-Widom fluctuations in 2D random Schrödinger operators//\\ Résumé : We construct a random Schrödinger operator on a subset of the hexagonal lattice and study its smallest positive eigenvalues. Using an asymptotic mapping, we relate them to the partition function of the directed polymer model on the square lattice. For a specific choice of the edge weight distribution, we obtain a model known as the log-Gamma polymer, which is integrable. Recent results about the fluctuations of free energy for the log-Gamma polymer allow us to prove Tracy-Widom type fluctuations for the smallest eigenvalue of the random Schrödinger operator. Joint with Balint Virag.\\ | * 14h00-15h00: **[[http://math.univ-lyon1.fr/~lancien/|Cécilia Lancien]]** //Random correlation matrices: when are they with high probability classical or quantum?// Two observers performing binary outcome measurements on subsystems of a global system may obtain more strongly correlated results when they have a shared entangled quantum state than when they only have shared randomness. This well-known phenomenon of so-called Bell inequality violation can be precisely characterized mathematically. Indeed, being a classical or a quantum correlation matrix exactly corresponds to being in the unit ball of some tensor norms. In this talk, I will start with explaining all this in details. I will then look at the following problem: given a random matrix of size n, can one estimate the typical value of its "classical" and "quantum" norms, as n becomes large? For a wide class of random matrices, the answer is yes, and shows a separation between the two values. This result may be interpreted as follows: in a typical direction, the borders of the sets of classical and quantum correlations are separated away from each other. Based on joint work with Carlos Gonzalez-Guillen, Carlos Palazuelos and Ignacio Villanueva: "Random quantum correlations are generically non-classical", Ann. Henri Poincaré, 18(12):3793-3813 (2017).\\ |
| * 15h30-16h30: **[[http://igor-kortchemski.perso.math.cnrs.fr/|Igor Kortchemski]]** //The geometry of random minimal factorizations of a long cycle//\\ Résumé : We will be interested in the structure of random typical minimal factorizations of the n-cycle into transpositions, which are factorizations of (1,...,n) as a product of n-1 transpositions. This is joint work with Valentin Féray.\\ | * 15h30-16h30: **[[http://pub.ist.ac.at/~dschroed/|Dominik Schröder]]** //Cusp Universality for Wigner-type Random Matrices.// For Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner-Dyson-Mehta universality conjecture for the last remaining universality type.\\ |
| ////\\ | |
| ===== Calendrier 2018-2019 ===== | ===== Calendrier 2018-2019 ===== |
| * Vendredi **12 Octobre**, salle 201 | * Vendredi **12 Octobre**, salle 201 |
| * 15h30-16h30: **[[http://igor-kortchemski.perso.math.cnrs.fr/|Igor Kortchemski]]** //The geometry of random minimal factorizations of a long cycle//\\ | * 15h30-16h30: **[[http://igor-kortchemski.perso.math.cnrs.fr/|Igor Kortchemski]]** //The geometry of random minimal factorizations of a long cycle//\\ |
| * Vendredi **11 Janvier**, salle 01 | * Vendredi **11 Janvier**, salle 01 |
| * 10h30-12h00: mini cours par **[[https://math.nyu.edu/~bourgade/|Paul Bourgade]]** ////\\ | * 10h30-12h00: mini cours par **[[https://math.nyu.edu/~bourgade/|Paul Bourgade]]** //Équations de boucles et champs log-corrélés//\\ |
| * 14h00-15h00: **[[http://google.com/search?q=Slim+Kammoun+math|Slim Kammoun]]** ////\\ | * 14h00-15h00: **[[http://google.com/search?q=Slim+Kammoun+math|Slim Kammoun]]** //Universality for random permutations//\\ |
| * 15h30-16h30: **[[https://people.kth.se/~holcomb/|Diane Holcomb]]** // //\\ | * 15h30-16h30: **[[https://people.kth.se/~holcomb/|Diane Holcomb]]** //On the centered maximum of the Sine beta process//\\ |
| * Vendredi **8 Février**, salle 201 | * Vendredi **8 Février**, salle 201 |
| * 10h30-12h00: mini cours par **[[https://www.math.u-psud.fr/~emaurel/|Édouard Maurel-Segala]]** // //\\ | * 10h30-12h00: mini cours par **[[https://www.math.u-psud.fr/~emaurel/|Édouard Maurel-Segala]]** //Étude de modèles de matrices par la méthode des cumulants libres//\\ |
| * 14h00-15h00: **[[https://sites.google.com/view/franck-gabriel-en/home|Franck Gabriel]]** ////\\ | * 14h00-15h00: **[[https://sites.google.com/view/franck-gabriel-en/home|Franck Gabriel]]** //Schur-Weyl-Jones duality and permutation-invariant random matrices//\\ |
| * 15h00-16h30: **[[https://www.math.uni-sb.de/ag/speicher/weber.html|Moritz Weber]]** ////\\ | * 15h30-16h30: **[[https://www.math.uni-sb.de/ag/speicher/weber.html|Moritz Weber]]** //Quantum symmetries of finite graphs and of noncommutative notions of independence//\\ |
| * Vendredi **15 Mars** salle 421 | * Vendredi **15 Mars** salle 421 |
| * mini cours par **[[https://www.di.ens.fr/~lelarge/|Marc Lelarge]]** ////\\ | * mini cours par **[[https://www.di.ens.fr/~lelarge/|Marc Lelarge]]** //The cavity method for the spiked Wigner model//\\ |
| * 14h00-15h00: **[[http://math.univ-lyon1.fr/~lancien/|Cécilia Lancien]]** ////\\ | * 14h00-15h00: **[[http://math.univ-lyon1.fr/~lancien/|Cécilia Lancien]]** //Random correlation matrices: when are they with high probability |
| * 15h30-14h30: **[[http://pub.ist.ac.at/~dschroed/|Dominik Schröder]]** ////\\ | classical or quantum?//\\ |
| | * 15h30-16h30: **[[http://pub.ist.ac.at/~dschroed/|Dominik Schröder]]** //Cusp Universality for Wigner-type Random Matrices//\\ |
| * pas de séance en **Avril** car Conférence du 15 au 19 à Luminy | * pas de séance en **Avril** car Conférence du 15 au 19 à Luminy |
| * Vendredi **10 Mai**, salle 314 | * Vendredi **10 Mai**, salle 314 |
| | * 14h00-15h00: **[[https://davidgarciaz.wixsite.com/math|David Garcia Zelada]]** ////\\ |
| | * 15h30-16h30: **[[https://www-m7.ma.tum.de/bin/view/Analysis/SimoneWarzel|Simone Warzel]]** ////\\ |
| * Vendredi **14 Juin**, salle 201 | * Vendredi **14 Juin**, salle 201 |
| * 14h00-15h00: **[[https://cims.nyu.edu/~dubach/|Guillaume Dubach]]** ////\\ | * 14h00-15h00: **[[https://cims.nyu.edu/~dubach/|Guillaume Dubach]]** ////\\ |
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| L'image tout en haut est tirée de [[https://www.mat.tuhh.de/forschung/aa/forschung.html]]. | L'image tout en haut est tirée de [[https://www.mat.tuhh.de/forschung/aa/forschung.html]]. |
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