Ci-dessous, les différences entre deux révisions de la page.
| Les deux révisions précédentes Révision précédente | Prochaine révisionLes deux révisions suivantes |
| mega:seminaire [2020/01/03 19:54] – [Calendrier 2019-2020] Guillaume BARRAQUAND | mega:seminaire [2020/01/04 23:08] – [Prochaine séance] Guillaume BARRAQUAND |
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| ===== Prochaine séance ===== | ===== Prochaine séance ===== |
| Vendredi **17 janvier**, salle 201 | Vendredi **17 janvier**, salle 201 |
| * 10h30-12h00: **[[https://webusers.imj-prg.fr/~frederic.klopp/|Frédéric Klopp]]**////\\ | * 10h30-12h00: **[[https://webusers.imj-prg.fr/~frederic.klopp/|Frédéric Klopp]]**// Localisation pour des opérateurs aléatoires//\\ |
| | Le cours présentera dans un cadre simple des éléments de la théorie spectrale des opérateurs aléatoires. Un phénomène emblématique de cette théorie est la localisation : les données spectrales, typiquement, valeurs propres et fonctions propres, bien qu'étant des objets globaux, ont une décorrélation spatiale rapide et sont ainsi déterminés par des caractéristiques locales. |
| * 14h00-15h00: **[[https://www.lpthe.jussieu.fr/~zuber/|Jean-Bernard Zuber]]**// A review of Horn's problem //\\ | * 14h00-15h00: **[[https://www.lpthe.jussieu.fr/~zuber/|Jean-Bernard Zuber]]**// A review of Horn's problem //\\ |
| Horn's problem deals with the following question: what can be said about the spectrum of eigenvalues of the sum C=A+B of two Hermitian matrices of given spectrum ? The support of the spectrum of C is now well understood, after a long series of works from Weyl (1912) to Horn (1952) to Klyachko (1998) and Knutson and Tao (1999). The problem has also amazing connections with group theory and the decomposition of tensor product of representations. \\ Comparison with the same problem for real symmetric matrices and the action of the orthogonal group reveals similarities but also unexpected differences... \\ In this talk, after a short introduction to the problem, I’ll sketch the computation of the probability distribution function of the eigenvalues of C, when A and B are independently and uniformly distributed on their orbit under the action of the group.\\ | Horn's problem deals with the following question: what can be said about the spectrum of eigenvalues of the sum C=A+B of two Hermitian matrices of given spectrum ? The support of the spectrum of C is now well understood, after a long series of works from Weyl (1912) to Horn (1952) to Klyachko (1998) and Knutson and Tao (1999). The problem has also amazing connections with group theory and the decomposition of tensor product of representations. \\ Comparison with the same problem for real symmetric matrices and the action of the orthogonal group reveals similarities but also unexpected differences... \\ In this talk, after a short introduction to the problem, I’ll sketch the computation of the probability distribution function of the eigenvalues of C, when A and B are independently and uniformly distributed on their orbit under the action of the group.\\ |