| Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente Prochaine révisionLes deux révisions suivantes |
| mega:seminaire [2020/05/14 20:56] – [Calendrier 2019-2020] Guillaume BARRAQUAND | mega:seminaire [2020/11/19 19:49] – [Prochaine séance] Guillaume BARRAQUAND |
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| * **Calendrier.** https://calendar.google.com/calendar/ical/qn5qq7dlmp38sc624s4png8umc%40group.calendar.google.com/public/basic.ics | * **Calendrier.** https://calendar.google.com/calendar/ical/qn5qq7dlmp38sc624s4png8umc%40group.calendar.google.com/public/basic.ics |
| ===== Prochaine séance ===== | ===== Prochaine séance ===== |
| Vendredi **15 mai**, en vidéoconférence via BigBlueButton, accessible par ce [[https://webconf.math.cnrs.fr/b/gui-cw9-efz|lien]], | Vendredi **11 décembre 2020**, en ligne. |
| * 14h00-15h00: **[[https://irma.math.unistra.fr/~vogel/|Martin Vogel]]**// Spectra of Toeplitz matrices subject to small random noise.//\\ | |
| Abstract: The spectra of nonselfadjoint linear operators can be very unstable and sensitive to small perturbations. This phenomenon is usually referred to as "pseudospectral effect". To explore this spectral instability we study the spectra of small random perturbations of non-selfadjoint operators in the case of Toeplitz matrices and in the case of the Toeplitz quantization of complex-valued functions on the torus. We will discuss recent results by Sjöstrand, Vogel and by Basak, Paquette and Zeitouni, describing the distribution of the eigenvalues in various regimes and settings. | **Matinée à suivre avec le lien** : /* http://www.animath.live/channel_A/index.php. \\ |
| * 15h30-16h30: **[[http://www.statslab.cam.ac.uk/~rb812/|Roland Bauerschmidt]]**// Random spanning forests and hyperbolic symmetry.//\\ | Pour communiquer, le chat se trouve ici http://www.animath.live/channel_A/chat.php et le salon BBB https://bbb.dma.ens.fr/b/nic-ez3-xfy.*/ |
| Abstract: We study (unrooted) random forests on a graph where the probability of a forest is multiplicatively weighted by a parameter $\beta>0$ per edge. This model is the $q\to 0$ limit of the random cluster model with $p=q\beta$. It is also known under different names such as the arboreal gas or the uniform forest model. In this talk, I will discuss the tantalizing conjectural behaviour of the model, and then present our result that there is no percolation in dimension two. This result relies on a surprising hyperbolic symmetry and methods previously developed for linearly reinforced walks. (This is joint work with Nick Crawford, Tyler Helmuth, and Andrew Swan.) | |
| ===== Calendrier 2019-2020 ===== | **Après-midi avec le lien** https://global.gotomeeting.com/join/542428485. Il est préférable d'utiliser le navigateur chrome/chromium ou le logiciel gotomeeting téléchargeable gratuitement. |
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| | * 10h30-12h00: mini cours par **[[https://math.nyu.edu/~serfaty/|Sylvia Serfaty]]**: //à venir.//\\ |
| | Résumé : |
| | * 14h00-15h00: **[[http://akrajenbrink.weebly.com/|Alexandre Krajenbrink]]** // Fredholm determinants, exact solutions to the Kardar-Parisi-Zhang equation and integro-differential Painlevé equations.//\\ |
| | Résumé : As Fredholm determinants are more and more frequent in the context of stochastic integrability, I discuss in this talk the existence of a common framework in many integrable systems where they appear. This consists in a hierarchy of equations, akin to the Zakharov-Shabat system, connecting an integro-differential extension of the Painlevé II hierarchy, the finite-time solutions of the Kardar-Parisi-Zhang equation and multi-critical fermions at finite temperature. |
| | The talk is based on the results of the paper arXiv:2008.01509 |
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| | * 15h00-15h30: ** Pause café **. // //\\ |
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| | * 15h30-16h30: **[[https://elliotpaquette.github.io/|Elliot Paquette]]** // The edge scaling limit of the Gaussian beta-ensemble characteristic polynomial.//\\ |
| | Résumé : The Gaussian beta-ensemble (GbetaE) is a 1-parameter generalization of the Gaussian orthogonal/unitary/symplectic ensembles which retains some integrable structure. Using this ensemble, in Ramirez, Rider and Virag constructed a limiting point process, the Airy-beta point process, which is the weak limit of the point process of eigenvalues in a neighborhood of the spectral edge. They constructed a limiting Sturm—Liouville problem, the stochastic Airy equation with Dirichlet boundary conditions, and they proved convergence of a discrete operator with spectra given by GbetaE to this limit. |
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| | Jointly with Gaultier Lambert, we give a construction of a new limiting object, the stochastic Airy function (SAi); we also show this is the limit of the characteristic polynomial of GbetaE in a neighborhood of the edge. It is the solution of the stochastic Airy equation, which is the usual Airy equation perturbed by a multiplicative white noise, with specified asymptotics at time=+infinity. Its zeros are given by the Airy-beta point process, and the mode of convergence we establish provides a new proof that Airy-beta is the limiting point process of eigenvalues of GbetaE. In this talk, we survey what new information we have on the characteristic polynomial; we show from where the stochastic Airy equation arises; we show how SAi is constructed; and we leave some unanswered questions. |
| | ===== Année 2020-2021 ===== |
| | * **Organisateurs 2020-2021.** |
| | * [[http://www.phys.ens.fr/~barraquand/|Guillaume Barraquand]] [[guillaume.barraquand@ens.fr. ]] et [[http://www.normalesup.org/~dumaz/|Laure Dumaz]] [[dumaz@ceremade.dauphine.fr]] |
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| | * Vendredi **13 novembre**, en ligne. |
| | * 10h30-12h00: mini cours par **[[http://rouault.perso.math.cnrs.fr/|Alain Rouault]]** //Analyse spectrale et grandes déviations. // |
| | * 14h00-15h00: **[[https://www.math.u-bordeaux.fr/~cmale/|Camille Male]]** // Applications of Freeness over the diagonal of large random matrices.// |
| | * 15h30-16h30: **[[http://lptms.u-psud.fr/gregory-schehr/|Gregory Schehr]]** // Exact persistence exponent for the 2d-diffusion equation: from random polynomials to truncated random matrices.//\\ |
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| | * Vendredi **11 décembre**, en ligne. |
| | * 10h30-12h00: mini cours par **[[https://math.nyu.edu/people/profiles/SERFATY_Sylvia.html|Sylvia Serfaty]]** // TBA.// |
| | * 14h00-15h00: **[[http://akrajenbrink.weebly.com/|Alexandre Krajenbrink]]** // Fredholm determinants, exact solutions to the Kardar-Parisi-Zhang equation and integro-differential Painlevé equations.// |
| | * 15h30-16h30: **[[https://elliotpaquette.github.io/|Elliot Paquette]]** // The edge scaling limit of the Gaussian beta-ensemble characteristic polynomial.//\\ |
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| | * Vendredi **15 janvier**, en ligne. **Attention, horaire inhabituel l'après midi.** |
| | * 10h30-12h00: mini cours par **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 15h00-16h00: **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 16h30-17h30: **[[https://www.math.wisc.edu/~valko/|Benedek Valkó]]** // TBA.//\\ |
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| | * Vendredi **5 février**, lieu à confirmer |
| | * 10h30-12h00: mini cours par **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 14h00-15h00: **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 15h30-16h30: **[[http://google.com/search?q=TBA|TBA]]** // TBA.//\\ |
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| | * Vendredi **12 mars**, amphi Hermite |
| | * 10h30-12h00: mini cours par **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 14h00-15h00: **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 15h30-16h30: **[[http://google.com/search?q=TBA|TBA]]** // TBA.//\\ |
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| | * Vendredi **9 avril**, amphi Hermite |
| | * 10h30-12h00: mini cours par **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 14h00-15h00: **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 15h30-16h30: **[[http://google.com/search?q=TBA|TBA]]** // TBA.//\\ |
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| | * Vendredi **7 mai**, amphi Hermite |
| | * 10h30-12h00: mini cours par **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 14h00-15h00: **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 15h30-16h30: **[[http://google.com/search?q=TBA|TBA]]** // TBA.//\\ |
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| | * Vendredi **11 juin**, lieu à confirmer |
| | * 10h30-12h00: mini cours par **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 14h00-15h00: **[[http://google.com/search?q=TBA|TBA]]** // TBA.// |
| | * 15h30-16h30: **[[http://google.com/search?q=TBA|TBA]]** // TBA.//\\ |
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| | ===== Année 2019-2020 ===== |
| * **Organisateurs 2019-2020.** | * **Organisateurs 2019-2020.** |
| * Matinée des thésards : [[http://google.com/search?q=Nathan+Noiry+ ceremade|Nathan Noiry]] [[noirynathan@gmail.com]] | * Matinée des thésards : [[http://google.com/search?q=Nathan+Noiry+ ceremade|Nathan Noiry]] [[noirynathan@gmail.com]] |
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| * Vendredi **5 juin**, en vidéoconférence. | * Vendredi **5 juin**, en vidéoconférence. |
| * 14h00-15h00: **[[http://google.com/search?q=Joseph+Najnudel|Joseph Najnudel]]** ////\\ | * 14h00-15h00: **[[http://google.com/search?q=Joseph+Najnudel|Joseph Najnudel]]** // The bead process for beta ensembles.//\\ |
| * 15h30-16h30: **[[https://sites.google.com/view/theoassiotis/publications|Theodoros Assiotis]]** ////\\ | * 15h30-16h30: **[[https://sites.google.com/view/theoassiotis/publications|Theodoros Assiotis]]** // Joint moments of the characteristic polynomial of a random unitary matrix.//\\ |
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