Différences
Ci-dessous, les différences entre deux révisions de la page.
Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente Prochaine révisionLes deux révisions suivantes | ||
mega:seminaire [2020/01/08 10:15] – Laure DUMAZ | mega:seminaire [2020/03/06 19:49] – [Calendrier 2019-2020] Guillaume BARRAQUAND | ||
---|---|---|---|
Ligne 13: | Ligne 13: | ||
* **Calendrier.** https:// | * **Calendrier.** https:// | ||
===== Prochaine séance ===== | ===== Prochaine séance ===== | ||
- | Vendredi **17 janvier**, salle 201 | + | Vendredi **13 mars**, amphi Darboux |
- | * 10h30-12h00: | + | * 10h30-12h00: |
- | Le cours présentera dans un cadre simple des éléments | + | Un processus ponctuel est dit rigide (ou number-rigide) si pour tout compact fixé, la donnée |
- | * 14h00-15h00: | + | * 14h00-15h00: |
- | 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 | + | Dans mon exposé, à partir de deux exemples liés à l'équation de Kardar-Parisi-Zhang |
- | If time permits, I'll also review some aspects of the connection with representation theory. | + | |
- | * 15h30-16h30: | + | * 15h30-16h30: |
- | Je décrirai une famille de mesures déterminantales sur la grassmannienne d'un espace euclidien, introduite dans un travail avec Thierry Lévy, et qui généralise la famille des processus ponctuels déterminantaux à noyau auto-adjoint. J' | + | In this talk, I would like to advertise an equality between two objects from very different areas of mathematical physics. This bridges the Gaussian Multiplicative Chaos, which plays an important role in certain conformal field theories, and a reference model in random matrices. The main tool is an explicit description in terms of coefficients known as |
+ | - canonical moments in statistics | ||
+ | - Verblunsky coefficients in the literature for orthogonal polynomials | ||
+ | - non-linear Fourier coefficients in harmonic analysis | ||
+ | On the one hand, in 1985, J.P Kahane introduced a random measure called the Gaussian Multiplicative Chaos (GMC), now an important object to in the study of turbulence. Morally, this is the measure whose Radon-Nikodym derivative w.r.t to Lebesgue is the exponential of a log correlated Gaussian field. In the cases of interest, this Gaussian field is a Schwartz distribution but not a function. As such, the construction of GMC needs to be done with care. In particular, in 2D, the GFF (Gaussian Free Field) is a random Schwartz distribution because of the logarithmic singularity of the Green kernel in 2D. Here we are interested in the 1D case on the circle. | ||
+ | On the other hand, it is known since Verblunsky (1930s) that a probability measure on the circle is entirely determined by the coefficients appearing in the recurrence of orthogonal polynomials. Furthermore, | ||
+ | The goal is to give a precise theorem whose loose form is CBE = GMC. Although it was known that random matrices exhibit log-correlated features, such an exact correspondence is quite a surprise. | ||
===== Calendrier 2019-2020 ===== | ===== Calendrier 2019-2020 ===== | ||
* **Organisateurs 2019-2020.** | * **Organisateurs 2019-2020.** | ||
Ligne 45: | Ligne 50: | ||
* Vendredi **7 février**, salle 421 le matin, amphi Hermite l' | * Vendredi **7 février**, salle 421 le matin, amphi Hermite l' | ||
- | * 10h30-12h00: | + | * 10h30-12h00: |
- | * 14h00-15h00: | + | * 14h00-15h00: |
- | * 15h30-16h30: | + | * 15h30-16h30: |
- | * Vendredi **13 mars**, | + | * Vendredi **13 mars**, |
- | * 10h30-12h00: | + | * 10h30-12h00: |
- | * 14h00-15h00: | + | * 14h00-15h00: |
- | * 15h30-16h30: | + | * 15h30-16h30: |
* Vendredi **3 avril**, salle 01 le matin, 314 l' | * Vendredi **3 avril**, salle 01 le matin, 314 l' | ||
* 10h30-12h00: | * 10h30-12h00: | ||
* 14h00-15h00: | * 14h00-15h00: | ||
- | * 15h30-16h30: | + | * 15h30-16h30: |
* Jeudi **7 mai** (attention jour différent !), salle 201 | * Jeudi **7 mai** (attention jour différent !), salle 201 | ||
* 10h30-12h00: | * 10h30-12h00: | ||
- | * 14h00-15h00: | + | * 14h00-15h00: |
* 15h30-16h30: | * 15h30-16h30: | ||
* Vendredi **5 juin**, salle 01 le matin, 314 l' | * Vendredi **5 juin**, salle 01 le matin, 314 l' | ||
- | * 10h30-12h00: | + | * 10h30-12h00: |
* 14h00-15h00: | * 14h00-15h00: | ||
* 15h30-16h30: | * 15h30-16h30: |