Ci-dessous, les différences entre deux révisions de la page.
| Les deux révisions précédentes Révision précédente | |
| mega:seminaire [2026/11/04 07:50] – Raphaël BUTEZ | mega:seminaire [2026/11/07 13:13] (Version actuelle) – Raphaël BUTEZ |
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| * 10h30-12h: mini cours de **[[https://djalil.chafai.net/|Djalil Chafaï]]** //On Poincaré inequalities for gases.// \\ | * 10h30-12h: mini cours de **[[https://djalil.chafai.net/|Djalil Chafaï]]** //On Poincaré inequalities for gases.// \\ |
| Abstract: This minicourse is about Poincaré inequalities for gases that appear as the equilibrium of Langevin dynamics. In particular, we discuss the optimal constants and functions for the Gaussian Unitary Ensemble and the complex Ginibre ensemble, following mostly https://arxiv.org/abs/1805.00708 and https://arxiv.org/abs/2608.19358. See also https://djalil.chafai.net/blog/2026/10/07/automatic-formalization-of-a-full-paper-in-lean/ | Abstract: This minicourse is about Poincaré inequalities for gases that appear as the equilibrium of Langevin dynamics. After the Gaussian case, via Hermite polynomials and via the Bakry-Émery curvature criterion, we explain how the center of mass of a gas with quadratic confinement splits off as an exact Gaussian factor. We use this to get the optimal Poincaré constant, with equality cases, for the Gaussian Unitary Ensemble, where the singular repulsion adds convexity, and for the complex Ginibre ensemble, which is not log-concave, and for which convexity is replaced by holomorphy through a Vandermonde transform and a flat Hörmander estimate in Bargmann-Fock space. Based mostly on https://arxiv.org/abs/1805.00708 and https://arxiv.org/abs/2608.19358, see also https://arxiv.org/abs/2608.17437 and https://djalil.chafai.net/blog/2026/10/07/automatic-formalization-of-a-full-paper-in-lean/ |
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