Large deviations for macroscopic observables of heavy-tailed matrices | Vidéo | Carmin.tv

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Large deviations for macroscopic observables of heavy-tailed matrices

By Alice Guionnet

Appears in collection : Chaire Jean Morlet - Conference - Algebraic aspects of random matrices / Chaire Jean Morlet - Conference - Aspects algébriques des matrices aléatoires

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.

Information about the video

Date of recording 08/10/2024
Date of publication 04/11/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20255103
Cite this video Guionnet, Alice (08/10/2024). Large deviations for macroscopic observables of heavy-tailed matrices. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20255103
URL https://dx.doi.org/10.24350/CIRM.V.20255103

Domain(s)

Probability

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

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