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Linear eigenvalue statistics of polynomials in a Wigner matrix and a diagonal deterministic matrix

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Authors : Dallaporta, Sandrine (Author of the conference)
CIRM (Publisher )

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Abstract : This talk will focus on the fluctuations of a linear spectral statistic around its mean for $P\left(W_N, D_N\right)$ where $P$ is a polynomial, $W_N$ a Wigner matrix and $D_N$ a deterministic diagonal matrix. I will first consider the case when $P\left(W_N,D_N\right)=W_N+D_N$, based on a joint work with M. Février (U. Paris-Saclay). In the general case of $P$ a selfadjoint noncommutative polynomial, I will present results for the special case of the Stieltjes transform, based on a joint work with S. Belinschi (CNRS, U. Toulouse), M. Capitaine (CNRS,U. Toulouse) and M. Février (U. Paris-Saclay).

Keywords : random matrices; free probability; linear eigenvalue statistics

MSC Codes :
60B20 - Random matrices (probabilistic aspects)
60F05 - Central limit and other weak theorems
15B52 - Random matrices

    Information on the Video

    Film maker : Recanzone, Luca
    Language : English
    Available date : 04/11/2024
    Conference Date : 10/10/2024
    Subseries : Research talks
    arXiv category : Probability
    Mathematical Area(s) : Probability & Statistics
    Format : MP4 (.mp4) - HD
    Video Time : 00:38:36
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-10-10_dallaporta.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.20255003
Cite this video as: Dallaporta, Sandrine (2024). Linear eigenvalue statistics of polynomials in a Wigner matrix and a diagonal deterministic matrix. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20255003
URI : http://dx.doi.org/10.24350/CIRM.V.20255003

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