English
Optimal global rigidity estimates in unitary invariant ensembles
Multi angle
Auteurs : Claeys, Tom (Auteur de la Conférence)
... (Editeur )
60B20 - Random matrices (probabilistic aspects)
15B52 - Random matrices
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2104/Slides/Claeys.pdf
... (Editeur )
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Résumé :
A fundamental question in random matrix theory is to understand how much the eigenvalues of a random matrix fluctuate.
I will address this question in the context of unitary invariant ensembles, by studying the global rigidity of the eigenvalues, or in other words the maximal deviation of an eigenvalue from its classical location.
Our approach to this question combines extreme value theory of log-correlated stochastic processes, and in particular the theory of multiplicative chaos, with asymptotic analysis of large Hankel determinants with Fisher-Hartwig symbols of various types.
In addition to optimal rigidity estimates, our approach sheds light on the extreme values and on the fractal geometry of the eigenvalue counting function.
The talk will be based on joint work in progress with Benjamin Fahs, Gaultier Lambert, and Christian Webb.
Codes MSC : I will address this question in the context of unitary invariant ensembles, by studying the global rigidity of the eigenvalues, or in other words the maximal deviation of an eigenvalue from its classical location.
Our approach to this question combines extreme value theory of log-correlated stochastic processes, and in particular the theory of multiplicative chaos, with asymptotic analysis of large Hankel determinants with Fisher-Hartwig symbols of various types.
In addition to optimal rigidity estimates, our approach sheds light on the extreme values and on the fractal geometry of the eigenvalue counting function.
The talk will be based on joint work in progress with Benjamin Fahs, Gaultier Lambert, and Christian Webb.
60B20 - Random matrices (probabilistic aspects)
15B52 - Random matrices
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2104/Slides/Claeys.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 09/05/2019 Date de captation : 08/04/2019 Sous collection : Research talks arXiv category : Mathematical Physics ; Probability Domaine : Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Durée : 00:52:27 Audience : Researchers Download : https://videos.cirm-math.fr/2019-04-08_Claeys.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial DataOrganisateurs de la rencontre : Basor, Estelle ; Bufetov, Alexander ; Cafasso, Mattia ; Grava, Tamara ; McLaughlin, Ken Dates : 08/04/2019 - 12/04/2019 Année de la rencontre : 2019 URL Congrès : https://www.chairejeanmorlet.com/2104.html
Données de citation
DOI : 10.24350/CIRM.V.19514603Citer cette vidéo: Claeys, Tom (2019). Optimal global rigidity estimates in unitary invariant ensembles. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19514603 URI : http://dx.doi.org/10.24350/CIRM.V.19514603 |
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