English
Local and global statistics for point sequences
Virtualconference
Auteurs : Aistleitner, Christoph (Auteur de la Conférence)
CIRM (Editeur )
11J54 - Small fractional parts of polynomials and generalizations
11J71 - Distribution modulo one
11K06 - General theory of distribution modulo 1
CIRM (Editeur )
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Résumé :
We recall some classical results for uniform distribution modulo one, and relate them with their counterparts in the "localized" setting of correlation functions and gap statistics. We discuss the difficulties arising from the localized setting, with a particular emphasis on questions concerning the almost everywhere behavior of parametric sequences. It turns out that in this metric setting one is naturally led to a Diophantine counting problem, which has interesting connections to additive combinatorics and to moment bounds for the Riemann zeta function.
Keywords : uniform distribution; pair correlation
Codes MSC : Keywords : uniform distribution; pair correlation
11J54 - Small fractional parts of polynomials and generalizations
11J71 - Distribution modulo one
11K06 - General theory of distribution modulo 1
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Informations sur la Vidéo
Réalisateur : Aistleitner, ChristophLangue : Anglais Date de publication : 30/11/2020 Date de captation : 30/11/2020 Sous collection : Research talks arXiv category : Number Theory Domaine : Number Theory Format : MP4 (.mp4) - HD Durée : 00:57:52 Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-19_Aistleitner.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2020 - Workshop: Discrepancy Theory and Applications - Part 1 / Chaire Jean-Morlet 2020 - Workshop : Théorie de la discrépance et applications - Part 1Organisateurs de la rencontre : Madritsch, Manfred ; Rivat, Joël ; Tichy, Robert Dates : 30/11/2020 - 01/12/2020 Année de la rencontre : 2020 URL Congrès : https://www.cirm-math.com/2257virtual.html
Données de citation
DOI : 10.24350/CIRM.V.19681203Citer cette vidéo: Aistleitner, Christoph (2020). Local and global statistics for point sequences. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19681203 URI : http://dx.doi.org/10.24350/CIRM.V.19681203 |
Voir aussi
- [Virtualconference] Greedy energy minimization and the van der Corput sequence (part 3) / Auteur de la Conférence Pausinger, Florian.
- [Virtualconference] Discrepancy of stratified samples from partitions of the unit cube (part 2) / Auteur de la Conférence Pausinger, Florian.
- [Virtualconference] Billiard orbits and geodesics in non-integrable flat dynamical systems (part 2) / Auteur de la Conférence Chen, William.
- [Virtualconference] Feynman Checkers: Number theory methods in quantum theory / Auteur de la Conférence Ustinov, Alexey ; Auteur de la Conférence Skopenkov, Mikhail.
- [Virtualconference] Pick's theorem and Riemann sums: a Fourier analytic tale / Auteur de la Conférence Travaglini, Giancarlo.
- [Virtualconference] On two different topics in discrepancy theory: From the discrepancy of stratified samples to greedy energy minimization (part 1) / Auteur de la Conférence Pausinger, Florian.
- [Virtualconference] Billiard orbits and geodesics in non-integrable flat dynamical systems (part 1) / Auteur de la Conférence Chen, William.
- [Virtualconference] On the interplay between uniform distribution, discrepancy, and energy minimization / Auteur de la Conférence Bilyk, Dmitriy.
Bibliographie
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