Matrices et graphes aléatoires / Random Matrices and Random Graphs

Collection Matrices et graphes aléatoires / Random Matrices and Random Graphs

Organizer(s) Capitaine, Mireille ; Knowles, Antti ; Maïda, Mylène ; Najim, Jamal

Date(s) 15/04/2019 - 19/04/2019

linked URL https://conferences.cirm-math.fr/1949.html

00:00:00 / 00:00:00

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Eigenvector convergence for minors of unitarily invariant infinite random matrices

By Joseph Najnudel

We give a new expression for the law of the eigenvalues of the discrete Anderson model on the finite interval [0, N], in terms of two random processes starting at both ends of the interval. Using this formula, we deduce that the tail of the eigenvectors behaves approximately like exponential of a Brownian motion with a drift. A similar result has recently been shown by B. Rifkind and B. Virag in the critical case, that is, when the random potential is multiplied by a factor 1/ √N.

Information about the video

Date of recording 18/04/2019
Date of publication 16/05/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19522603
Cite this video Najnudel, Joseph (18/04/2019). Eigenvector convergence for minors of unitarily invariant infinite random matrices. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19522603
URL https://dx.doi.org/10.24350/CIRM.V.19522603

Domain(s)

Probability

Bibliography

BORODIN, Alexei et OLSHANSKI, Grigori. Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes. Annals of mathematics, 2005, p. 1319-1422. - https://www.jstor.org/stable/3597358
QIU, Yanqi. Infinite random matrices & ergodic decomposition of finite and infinite Hua–Pickrell measures. Advances in Mathematics, 2017, vol. 308, p. 1209-1268. - https://doi.org/10.1016/j.aim.2017.01.003
BOURGADE, Paul, NAJNUDEL, Joseph, et NIKEGHBALI, Ashkan. A unitary extension of virtual permutations. International Mathematics Research Notices, 2013, vol. 2013, no 18, p. 4101-4134. - https://doi.org/10.1093/imrn/rns167
MAPLES, Kenneth, NAJNUDEL, Joseph, et NIKEGHBALI, Ashkan. Limit operators for circular ensembles. arXiv preprint arXiv:1304.3757, 2013. - https://arxiv.org/abs/1304.3757
NAJNUDEL, Joseph. Eigenvector convergence for minors of unitarily invariant infinite random matrices. arXiv preprint arXiv:1810.02983, 2018. - https://arxiv.org/abs/1810.02983

MSC codes

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