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:start [2018/01/09 15:23] – [Exposés 2017-2018] male | mega:start [2018/01/22 11:55] – [Exposés 2017-2018] male |
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| * Vendredi **12 janvier** | * Vendredi **12 janvier** |
| * 10h30-12h00: mini cours par **[[http://www.camillemale.com|Camille Male]]** sur les méthodes non commutatives en matrices aléatoires | * 10h30-12h00: mini cours par **[[http://www.camillemale.com|Camille Male]]** sur les méthodes non commutatives en matrices aléatoires |
| * 14h30-15h45: **[[https://sites.google.com/site/torbenkruegermath/|Torben Krüger]]** //Random matrices with slow correlation decay \\ // The resolvent of a large dimensional self-adjoint random matrix approximately satisfies the matrix Dyson equation (MDE) up to a random error. We show that for random matrices with arbitrary expectation and slow decay of correlation among its entries this error matrix converges to zero both in an isotropic and averaged sense with optimal rates of convergence as the dimension tends to infinity. This result requires a delicate cancellation (self-energy renormalization) which is seen through a diagrammatic cumulant expansion that automatically exploits the cancellation to all orders. Furthermore, we provide a comprehensive isotropic stability analysis of the MDE down to the length scale of the eigenvalue spacing. This analysis is then used to show convergence of the resolvent to the non-random solution of the MDE and to prove that the local eigenvalue statistics are universal, i.e. they do not depend on the distribution of the entries of the random matrix under consideration (Wigner-Dyson-Mehta spectral universality). Joint work with Oskari Ajanki & Laszlo Erdös & Dominik Schröder. | * 14h30-15h45: **[[https://sites.google.com/site/torbenkruegermath/|Torben Krüger]]** //Random matrices with slow correlation decay \\ // |
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| * 15h45-17h00: **[[http://www.iecl.univ-lorraine.fr/~Jeremie.Unterberger/|Jérémie Unterberger]]** //Global fluctuations for 1D log-gas dynamics\\ // We discuss in this lecture the hydrodynamic limit in the macroscopic regime of a coupled system of stochastic differential equations describing the noisy dynamics of N point particles submitted to the sum of an arbitrary one-body potential and of a logarithmic two-body potential, sometimes called generalized Dyson's Brownian motion. The equilibrium measure is that of a beta-ensemble, and static, equilibrium fluctuations have been determined by Johansson. The limit when N goes to infinity of this system is known to satisfy a mean-field Mac-Kean Vlasov equation. We prove that, for suitable initial conditions, fluctuations around the deterministic limit are Gaussian and satisfy an explicit PDE, which can be solved using characteristic equations in the complex plane. We also point at possible connections to results due to Duits (concerning non-colliding processes) and Dubail-Calabrese-Stéphan-Viti (concerning fermion gases in a confining potential). | * 15h45-17h00: **[[http://www.iecl.univ-lorraine.fr/~Jeremie.Unterberger/|Jérémie Unterberger]]** //Global fluctuations for 1D log-gas dynamics\\ // |
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| * Vendredi **9 février** | * Vendredi **9 février** |
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| * Vendredi **11 mai** | * Vendredi **11 mai** |
| | * 10h30-12h00: mini cours par **[[http://google.com/search?q=Maxime+Février+Maths|Maxime Février]]** |
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| * Vendredi **8 juin** | * Vendredi **8 juin** |