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 [2020/11/12 14:46] – Laure DUMAZ | ||
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* **Calendrier.** https:// | * **Calendrier.** https:// | ||
===== Prochaine séance ===== | ===== Prochaine séance ===== | ||
- | Vendredi **13 mars**, amphi Darboux | + | Vendredi **13 novembre 2020**, en ligne. |
- | * 10h30-12h00: | + | |
- | Un processus ponctuel est dit rigide (ou number-rigide) si pour tout compact fixé, la donnée | + | **Matinée à suivre avec le lien** : http:// |
- | * 14h00-15h00: | + | Pour communiquer, |
- | Dans mon exposé, à partir de deux exemples liés à l' | + | |
+ | **Après-midi avec le lien** https:// | ||
+ | |||
+ | |||
+ | * 10h30-12h00: | ||
+ | Résumé : Dans la théorie des polynômes orthogonaux, les règles | ||
+ | Dans ce mini-cours, je donnerai une introduction historique depuis | ||
+ | * 14h00-15h00: | ||
+ | Résumé : Traffic probability is an extension of free probability that comes with a general notion of traffic independence. This notion encodes a large class of relation, in particular all non commutative notions of independence. For a long time, this notion had only a combinatorial presentation, | ||
+ | - a general asymptotic freeness theorem for a very general class of random matrices | ||
+ | - a method for computing outliers in spiked random matrix models with a variance profile | ||
+ | - a characterization of the fluctuations of linear statistics for large Wigner matrices. | ||
+ | * 15h00-15h30: | ||
+ | |||
+ | * 15h30-16h30: | ||
+ | to truncated random matrices.// | ||
+ | Résumé : After an introduction to persistence probabilities and related first-passage time in statistical physics, I will discuss a specific example: the 2d diffusion equation with random initial conditions. The persistence probability in this problem turns out to be related to the probability of no real root for Kac random polynomials. I will show that this probability can be computed by using yet another connection, namely to the truncated orthogonal ensemble of random matrices. | ||
+ | |||
+ | ===== Année 2020-2021 ===== | ||
+ | * **Organisateurs 2020-2021.** | ||
+ | * [[http:// | ||
+ | |||
+ | * Vendredi **13 novembre**, en ligne | ||
+ | * 10h30-12h00: | ||
+ | * 14h00-15h00: | ||
+ | * 15h30-16h30: | ||
+ | |||
+ | |||
+ | |||
+ | Les dates des séances suivantes seront confirmées prochainement. | ||
+ | |||
+ | * Vendredi **11 décembre**, lieu à confirmer | ||
+ | * 10h30-12h00: | ||
+ | * 14h00-15h00: | ||
+ | * 15h30-16h30: | ||
+ | |||
+ | * Vendredi **15 janvier**, lieu à confirmer | ||
+ | * 10h30-12h00: mini cours par **[[http:// | ||
+ | * 14h00-15h00: **[[http:// | ||
+ | * 15h30-16h30: | ||
+ | |||
+ | |||
+ | * Vendredi **5 février**, lieu à confirmer | ||
+ | * 10h30-12h00: | ||
+ | * 14h00-15h00: | ||
+ | * 15h30-16h30: | ||
+ | |||
+ | |||
+ | * Vendredi **12 mars**, amphi Hermite | ||
+ | * 10h30-12h00: | ||
+ | * 14h00-15h00: | ||
+ | * 15h30-16h30: | ||
+ | |||
+ | * Vendredi **9 avril**, amphi Hermite | ||
+ | * 10h30-12h00: | ||
+ | * 14h00-15h00: | ||
+ | * 15h30-16h30: | ||
+ | |||
+ | * Vendredi **7 mai**, amphi Hermite | ||
+ | * 10h30-12h00: | ||
+ | * 14h00-15h00: | ||
+ | * 15h30-16h30: | ||
+ | |||
+ | * Vendredi **11 juin**, lieu à confirmer | ||
+ | * 10h30-12h00: | ||
+ | * 14h00-15h00: | ||
+ | * 15h30-16h30: | ||
- | * 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:// | ||
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* 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: | + | |