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H 1 Conditioned determinantal processes are determinantal

Auteurs : Shamov, Alexander (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : A determinantal point process governed by a Hermitian contraction kernel $K$ on a measure space $E$ remains determinantal when conditioned on its configuration on a subset $B \subset E$. Moreover, the conditional kernel can be chosen canonically in a way that is "local" in a non-commutative sense, i.e. invariant under "restriction" to closed subspaces $L^2(B) \subset P \subset L^2(E)$. Using the properties of the canonical conditional kernel we establish a conjecture of Lyons and Peres: if $K$ is a projection then almost surely all functions in its image can be recovered by sampling at the points of the process.
    Joint work with Alexander Bufetov and Yanqi Qiu.

    Codes MSC :
    60C05 - Combinatorial probability
    60G55 - Point processes

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 10/03/17
      Date de captation : 27/02/17
      Collection : Research talks ; Analysis and its Applications ; Dynamical Systems and Ordinary Differential Equations ; Mathematical Physics ; Probability and Statistics
      Format : MP4
      Durée : 00:40:09
      Domaine : Dynamical Systems & ODE ; Probability & Statistics ; Mathematical Physics ; Analysis and its Applications
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-02-27_Shamov.mp4

    Informations sur la rencontre

    Nom de la rencontre : Random matrices and determinantal process / Matrices aléatoires. Processus déterminantaux
    Organisateurs de la rencontre : Bufetov, Alexander ; Chhaibi, Reda ; Grava, Tamara ; Kuijlaars, Arno ; Krasovsky, Igor ; Nikitin, Pavel ; Savin, Dmitry
    Dates : 27/02/17 - 03/03/17
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1715.html

    Citation Data

    DOI : 10.24350/CIRM.V.19134203
    Cite this video as: Shamov, Alexander (2017). Conditioned determinantal processes are determinantal. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19134203
    URI : http://dx.doi.org/10.24350/CIRM.V.19134203

    Voir aussi


    1. Bufetov, A.I., Qiu, Y., & Shamov, A. (2016). Kernels of conditional determinantal measures. - https://arxiv.org/abs/1612.06751

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