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| Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente Prochaine révisionLes deux révisions suivantes |
| mega:start [2017/10/10 14:20] – Laure DUMAZ | mega:start [2017/12/01 12:02] – [Exposés à venir 2017-2018] male |
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| * Vendredi **8 décembre** | * Vendredi **8 décembre** |
| * 14h30-15h45: **[[http://perso.ens-lyon.fr/aguionne/|Alice Guionnet]]** // \\ // | * 14h30-15h45: **[[https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/Fyodorovy.aspx|Yan Fyodorov]]** //On statistics of bi-orthogonal eigenvectors in real and complex Ginibre ensembles combining partial Schur decomposition with supersymmetry.\\ //I will present a method of studying the joint probability density (JPD) of an eigenvalue and the associated 'non-orthogonality overlap factor' (also known as the condition number) of the left and right eigenvectors for non-selfadjoint random matrices. First we derive the general finite size N expression for the JPD of a real eigenvalue and the associated non-orthogonality factor in the real Ginibre ensemble, and then analyze its 'bulk' and 'edge' scaling limits. The ensuing distribution is maximally heavy-tailed, so that all integer moments beyond normalization are divergent. A similar calculation for a complex eigenvalue and the associated non-orthogonality factor in the complex Ginibre ensemble will be presented as well and yields a distribution with the finite first moment. Its 'bulk' scaling limit yields a distribution whose first moment reproduces the well-known result of Chalker and Mehlig , and I provide the 'edge' scaling distribution for this case as well. The method involves evaluating the ensemble average of products and ratios of integer and half-integer powers of characteristic polynomials for Ginibre matrices, which is performed in the framework of the supersymmetry approach. These results complement recent studies by P. Bourgade & G. Dubach. |
| * 15h45-17h00: **[[https://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/Fyodorovy.aspx|Yan Fyodorov]]** //On statistics of bi-orthogonal eigenvectors in real and complex Ginibre ensembles combining partial Schur decomposition with supersymmetry.\\ //I will present a method of studying the joint probability density (JPD) of an eigenvalue and the associated 'non-orthogonality overlap factor' (also known as the condition number) of the left and right eigenvectors for non-selfadjoint random matrices. First we derive the general finite size N expression for the JPD of a real eigenvalue and the associated non-orthogonality factor in the real Ginibre ensemble, and then analyze its 'bulk' and 'edge' scaling limits. The ensuing distribution is maximally heavy-tailed, so that all integer moments beyond normalization are divergent. A similar calculation for a complex eigenvalue and the associated non-orthogonality factor in the complex Ginibre ensemble will be presented as well and yields a distribution with the finite first moment. Its 'bulk' scaling limit yields a distribution whose first moment reproduces the well-known result of Chalker and Mehlig , and I provide the 'edge' scaling distribution for this case as well. The method involves evaluating the ensemble average of products and ratios of integer and half-integer powers of characteristic polynomials for Ginibre matrices, which is performed in the framework of the supersymmetry approach. These results complement recent studies by P. Bourgade & G. Dubach. | * 15h45-17h00: **[[http://perso.ens-lyon.fr/aguionne/|Alice Guionnet]]** //Fluctuations pour les pavages aleatoires et equations de Nekrasov \\ //Lozenge random tiling converge as the size of the tiles go to zero to a deterministic shape for a wide variety of domains. This shape has regions were the tiles are fully packed (the so-called void or frozen regions) and regions where more choices are available, the so-called liquid region. The fluctuations of these regions, and in particular of the frozen boundary, are known to follow the Tracy-Widom laws appearing in random matrix theory for nice domains. We will discuss how to prove such a result for domains constructed by gluing trapezoids, for which the distribution of tiles is given by a discrete coulomb gas. Introducing more general domains called the discrete Beta-ensembles, we will discuss universal local fluctuations of extreme particles for these models and relate it to the fluctuations in continuous Beta-models. The main tool to approach these questions are Nekrasov's equations.This talk is based on join works with Borodin, Borot,Gorin and Huang. |
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| * Vendredi **12 janvier** | * Vendredi **12 janvier** |
| | * 14h30-15h45: **[[https://sites.google.com/site/torbenkruegermath/|Torben Krüger]]** // \\ // |
| | * 15h45-17h00: **[[http://www.iecl.univ-lorraine.fr/~Jeremie.Unterberger/|Jérémie Unterberger]]** |
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| * Vendredi **9 février** | * Vendredi **9 février** |