Eigenvector convergence for minors of unitarily invariant infinite random matrices | Vidéo | Carmin.tv

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Eigenvector convergence for minors of unitarily invariant infinite random matrices

De Joseph Najnudel

Apparaît dans la collection : Matrices et graphes aléatoires / Random Matrices and Random Graphs

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.

Informations sur la vidéo

Date de captation 18/04/2019
Date de publication 16/05/2019
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19522603
Citer cette vidéo 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

Domaine(s)

Probabilités

Bibliographie

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

Codes MSC

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