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H 1 Metric discrepancy theory

Auteurs : Tichy, Robert (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : This is a survey on progress in metric discrepancy theory and probabilistic aspects in harmonic analysis. We start with classical limit theorems of Salem and Zygmund as well as with the work of Erdoes and Gaal and of Walter Philipp. A focus lies on laws of the iterated logarithm for discrepancy functions of lacunary sequences. We show the connection to certain diophantine properties of the underlying lacunary sequences obtaining precise asymptotic formulas. Different phenomena for subexponentially growing, for exponentially growing and for superexponentially growing sequences are established. Furthermore, relations to arithmetic dynamical systems and to Donald Knuth`s concept of pseudorandomness are discussed. Recent results are contained in joint work with Christoph Aistleitner and Istvan Berkes and it is planed to publish parts of it in a Jean Morlet Springer lecture Notes volume.

    Keywords : discrepancy; limit laws; lacunary sequences; Diophantine equations

    Codes MSC :
    11J83 - Metric theory of numbers
    11K38 - Irregularities of distribution, discrepancy
    11K60 - Diophantine approximation (probabilistic number theory)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 22/01/2021
      Date de captation : 04/02/2021
      Collection : Research talks
      Format : MP4
      Durée : 00:55:51
      Domaine : Analysis and its Applications ; Number Theory ; Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2021-02-04_Tichy.mp4

    Informations sur la rencontre

    Nom de la rencontre : Jean-Morlet Chair 2020 (2) - Workshop: Discrepancy Theory and Applications - Part 2 / Chaire Jean-Morlet 2020 (2) - Workshop : Théorie de la discrépance et applications - Part 2
    Organisateurs de la rencontre : Madritsch, Manfred ; Rivat, Joël ; Tichy, Robert
    Dates : 04/02/2021 - 05/02/2021
    Année de la rencontre : 2021
    URL Congrès : https://www.chairejeanmorlet.com/2641.html

    Citation Data

    DOI : 10.24350/CIRM.V.19715003
    Cite this video as: Tichy, Robert (2021). Metric discrepancy theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19715003
    URI : http://dx.doi.org/10.24350/CIRM.V.19715003

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