En poursuivant votre navigation sur ce site, vous acceptez l'utilisation d'un simple cookie d'identification. Aucune autre exploitation n'est faite de ce cookie. OK
1

Large deviations for macroscopic observables of heavy-tailed matrices

Bookmarks Report an error
Multi angle
Authors : Guionnet, Alice (Author of the conference)
CIRM (Publisher )

Loading the player...

Abstract : We consider independent Hermitian heavy-tailed random matrices. Our model includes the Lévy matrices as well as sparse random matrices with O(1) non-zero entries per row. By representing these matrices as weighted graphs, we derive a large deviation principle for key macroscopic observables. Specifically, we focus on the empirical distribution of eigenvalues, the joint neighborhood distribution, and the joint traffic distribution. As an application, we define a notion of microstates entropy for traffic distribution which is additive under free traffic convolution.

Keywords : random matrices; large deviations; free probability

MSC Codes :
46L54 - Free probability and free operator algebras
60B20 - Random matrices (probabilistic aspects)
60F10 - Large deviations

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 04/11/2024
    Conference Date : 08/10/2024
    Subseries : Research talks
    arXiv category : Probability
    Mathematical Area(s) : Probability & Statistics
    Format : MP4 (.mp4) - HD
    Video Time : 00:44:48
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-10-08_Guionnet.mp4

Information on the Event

Event Title : Chaire Jean Morlet - Conference - Algebraic aspects of random matrices / Chaire Jean Morlet - Conference - Aspects algébriques des matrices aléatoires
Event Organizers : Bordenave, Charles ; Capitaine, Mireille ; Chhaibi, Reda ; Collins, Benoît ; Defosseux, Manon ; Demni, Nizar
Dates : 07/10/2024 - 11/10/2024
Event Year : 2024
Event URL : https://conferences.cirm-math.fr/3052.html

Citation Data

DOI : 10.24350/CIRM.V.20255103
Cite this video as: Guionnet, Alice (2024). Large deviations for macroscopic observables of heavy-tailed matrices. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20255103
URI : http://dx.doi.org/10.24350/CIRM.V.20255103

See Also

Bibliography

  • BORDENAVE, Charles, GUIONNET, Alice, et MALE, Camille. Large deviations for macroscopic observables of heavy-tailed matrices. arXiv preprint arXiv:2409.14027, 2024. - https://doi.org/10.48550/arXiv.2409.14027



Imagette Video

Bookmarks Report an error