Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data

Collection Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data

Organizer(s) Basor, Estelle ; Bufetov, Alexander ; Cafasso, Mattia ; Grava, Tamara ; McLaughlin, Ken

Date(s) 08/04/2019 - 12/04/2019

linked URL https://www.chairejeanmorlet.com/2104.html

00:00:00 / 00:00:00

2 22

Optimal global rigidity estimates in unitary invariant ensembles

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.

Information about the video

Date of recording 08/04/2019
Date of publication 09/05/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19514603
Cite this video Claeys, Tom (08/04/2019). Optimal global rigidity estimates in unitary invariant ensembles. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19514603
URL https://dx.doi.org/10.24350/CIRM.V.19514603

Domain(s)

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2104/Slides/Claeys.pdf

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