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H 1 Eigenvector convergence for minors of unitarily invariant infinite random matrices

Auteurs : Najnudel, Joseph (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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.

    Codes MSC :
    60B20 - Random matrices (probabilistic aspects)
    65F15 - Eigenvalues, eigenvectors

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 16/05/2019
      Date de captation : 18/04/2019
      Collection : Exposés de recherche
      Format : MP4
      Durée : 00:32:10
      Domaine : Algebra ; Combinatorics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-04-18_Najnudel.mp4

    Informations sur la rencontre

    Nom de la rencontre : Matrices et graphes aléatoires / Random Matrices and Random Graphs
    Organisateurs de la rencontre : Capitaine, Mireille ; Knowles, Antti ; Maïda, Mylène ; Najim, Jamal
    Dates : 15/04/2019 - 19/04/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/1949.html

    Citation Data

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


    Voir aussi

    Bibliographie

    1. 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

    2. 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

    3. 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

    4. MAPLES, Kenneth, NAJNUDEL, Joseph, et NIKEGHBALI, Ashkan. Limit operators for circular ensembles. arXiv preprint arXiv:1304.3757, 2013. - https://arxiv.org/abs/1304.3757

    5. NAJNUDEL, Joseph. Eigenvector convergence for minors of unitarily invariant infinite random matrices. arXiv preprint arXiv:1810.02983, 2018. - https://arxiv.org/abs/1810.02983

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