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H 1 A functional limit theorem for the sine-process

Auteurs : Dymov, Andrey (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : It is well-known that a large class of determinantal processes including the sine-process satisfies the Central Limit Theorem. For many dynamical systems satisfying the CLT the Donsker Invariance Principle also takes place. The latter states that, in some appropriate sense, trajectories of the system can be approximated by trajectories of the Brownian motion. I will present results of my joint work with A. Bufetov, where we prove a functional limit theorem for the sine-process, which turns out to be very different from the Donsker Invariance Principle. We show that the anti-derivative of our process can be approximated by the sum of a linear Gaussian process and small independent Gaussian fluctuations whose covariance matrix we compute explicitly.

    Codes MSC :
    60F05 - Central limit and other weak theorems
    60G55 - Point processes
    60G60 - Random fields

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 08/03/17
      Date de captation : 28/02/17
      Collection : Research talks ; Dynamical Systems and Ordinary Differential Equations ; Mathematical Physics ; Probability and Statistics
      Format : MP4
      Durée : 00:43:02
      Domaine : Dynamical Systems & ODE ; Mathematical Physics ; Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-02-28_Dymov.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.19134403
    Cite this video as: Dymov, Andrey (2017). A functional limit theorem for the sine-process . CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19134403
    URI : http://dx.doi.org/10.24350/CIRM.V.19134403

    Voir aussi


    1. Bufetov, A.I., & Dymov, A.V. (2016). A functional limit theorem for the sine-process. - https://arxiv.org/abs/1701.00111

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