| Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente |
| mega:seminaire [2024/03/23 17:08] – [Prochaine séance] Guillaume BARRAQUAND | mega:seminaire [2024/03/23 23:34] (Version actuelle) – [Prochaine séance] Guillaume BARRAQUAND |
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| * 10h30-12h: mini cours par **[[https://djalil.chafai.net/wiki/|Djalil Chafaï]]** //à venir.// | * 10h30-12h: mini cours par **[[https://djalil.chafai.net/wiki/|Djalil Chafaï]]** //Logarithmic Sobolev inequalities.// |
| Abstract: | Abstract: This mini-course is an introduction to logarithmic Sobolev inequalities. We will |
| | present the links with hypercontractivity of Markov semigroups, the long time behavior of |
| | ergodic Markov processes, and the concentration of measure phenomenon. In a second part, |
| | we will present some links with beta ensembles, Wigner random matrices, and Dyson brownian motion. |
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| * 14h00-15h00: Séminaire de **[[https://scholar.google.com/citations?user=bnQNt98AAAAJ&hl=ja|Yuan, Wangjun]]** //Hitting probability of Gaussian random fields and collision of eigenvalues of random matrices.// | * 14h00-15h00: Séminaire de **[[https://scholar.google.com/citations?user=bnQNt98AAAAJ&hl=ja|Yuan, Wangjun]]** //Hitting probability of Gaussian random fields and collision of eigenvalues of random matrices.// |
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| * 15h30-16h30: Séminaire de **[[https://sites.google.com/view/aronwennman/home|Aron Wennman]]** //à venir.// | * 15h30-16h30: Séminaire de **[[https://sites.google.com/view/aronwennman/home|Aron Wennman]]** //A PDE approach to polynomial Bergman kernels and planar orthogonal polynomials.// |
| Abstract: | Abstract: In this talk I plan to describe some (old and new) results about orthogonal polynomials and polynomial reproducing kernel functions, defined with respect to weighted area measure on the plane. These objects appear naturally in connection with the 2D Coulomb gas at a particular inverse temperature, and they have recently been used to obtain several universality results for this model. |
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| | I will describe a number of equivalent characterisations of planar orthogonality, each offering its own inroad to study large-degree asymptotics. I will then focus on one recent PDE based approach which shares some resemblance with the Riemann-Hilbert approach to orthogonal polynomials on the real line. One of the main results is a surprisingly simple global asymptotic formula for the one-point function (for finite N). |
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| | The talk is based on joint work with Hedenmalm (KTH) and work in progress with Giandinoto (Stockholm University). |
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| ===== Année 2023-2024 ===== | ===== Année 2023-2024 ===== |