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 [2020/04/01 12:26] – [Calendrier 2019-2020] Guillaume BARRAQUAND | mega:seminaire [2020/10/07 19:26] – [Année 2020-2021] Guillaume BARRAQUAND | ||
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Ligne 13: | Ligne 13: | ||
* **Calendrier.** https:// | * **Calendrier.** https:// | ||
===== Prochaine séance ===== | ===== Prochaine séance ===== | ||
- | Vendredi **13 mars**, amphi Darboux | + | Vendredi **13 novembre 2020**, amphi Hermite (l' |
- | * 10h30-12h00: | + | * 10h30-12h00: |
- | Un processus ponctuel est dit rigide (ou number-rigide) si pour tout compact fixé, la donnée de la configuration à l' | + | Résumé : |
- | * 14h00-15h00: | + | * 14h00-15h00: |
- | Dans mon exposé, à partir de deux exemples liés à l' | + | Résumé : TBA. |
+ | * 15h30-16h30: | ||
+ | Résumé : TBA. | ||
+ | |||
+ | ===== Année 2020-2021 ===== | ||
+ | * **Organisateurs 2020-2021.** | ||
+ | * [[http:// | ||
+ | |||
+ | * Vendredi **13 novembre**, amphi Hermite | ||
+ | * 10h30-12h00: | ||
+ | * 14h00-15h00: | ||
+ | * 15h30-16h30: | ||
+ | |||
+ | Les dates des séances suivantes seront confirmées prochainement. | ||
- | * 15h30-16h30: | + | ===== Année |
- | 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 | + | |
* **Organisateurs 2019-2020.** | * **Organisateurs 2019-2020.** | ||
* Matinée des thésards : [[http:// | * Matinée des thésards : [[http:// | ||
Ligne 63: | Ligne 68: | ||
* 15h30-16h30: | * 15h30-16h30: | ||
- | * Jeudi **7 mai** (attention jour différent !), | + | * Vendredi |
- | * 10h30-12h00: | + | * 14h00-15h00: |
- | * 14h00-15h00: | + | * 15h30-16h30: |
- | * 15h30-16h30: | + | |
- | * Vendredi **5 juin**, | + | * Vendredi **5 juin**, |
- | * 10h30-12h00: | + | * 14h00-15h00: |
- | * 14h00-15h00: | + | * 15h30-16h30: |
- | * 15h30-16h30: | + | |