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Optimal global rigidity estimates in unitary invariant ensembles
Multi angle
Authors : Claeys, Tom (Author of the conference)
CIRM (Publisher )
60B20 - Random matrices (probabilistic aspects)
15B52 - Random matrices
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/Claeys.pdf
CIRM (Publisher )
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Abstract :
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.
MSC Codes : 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
Additional resources :
https://www.cirm-math.fr/RepOrga/2104/Slides/Claeys.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 09/05/2019 Conference Date : 08/04/2019 Subseries : Research talks arXiv category : Mathematical Physics ; Probability Mathematical Area(s) : Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:52:27 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-04-08_Claeys.mp4 
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Information on the Event
Event Title : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial DataEvent Organizers : Basor, Estelle ; Bufetov, Alexander ; Cafasso, Mattia ; Grava, Tamara ; McLaughlin, Ken Dates : 08/04/2019 - 12/04/2019 Event Year : 2019 Event URL : https://www.chairejeanmorlet.com/2104.html
Citation Data
DOI : 10.24350/CIRM.V.19514603Cite this video as: 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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