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Local and global statistics for point sequences
Virtualconference
Authors : Aistleitner, Christoph (Author of the conference)
CIRM (Publisher )
11J54 - Small fractional parts of polynomials and generalizations
11J71 - Distribution modulo one
11K06 - General theory of distribution modulo 1
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Aistleitner, ChristophLanguage : English Available date : 30/11/2020 Conference Date : 30/11/2020 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:57:52 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-19_Aistleitner.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair 2020 - Workshop: Discrepancy Theory and Applications - Part 1 / Chaire Jean-Morlet 2020 - Workshop : Théorie de la discrépance et applications - Part 1Event Organizers : Madritsch, Manfred ; Rivat, Joël ; Tichy, Robert Dates : 30/11/2020 - 01/12/2020 Event Year : 2020 Event URL : https://www.cirm-math.com/2257virtual.html
Citation Data
DOI : 10.24350/CIRM.V.19681203Cite this video as: 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 |
See Also
- [Virtualconference] Greedy energy minimization and the van der Corput sequence (part 3) / Author of the conference Pausinger, Florian.
- [Virtualconference] Discrepancy of stratified samples from partitions of the unit cube (part 2) / Author of the conference Pausinger, Florian.
- [Virtualconference] Billiard orbits and geodesics in non-integrable flat dynamical systems (part 2) / Author of the conference Chen, William.
- [Virtualconference] Feynman Checkers: Number theory methods in quantum theory / Author of the conference Ustinov, Alexey ; Author of the conference Skopenkov, Mikhail.
- [Virtualconference] Pick's theorem and Riemann sums: a Fourier analytic tale / Author of the conference Travaglini, Giancarlo.
- [Virtualconference] On two different topics in discrepancy theory: From the discrepancy of stratified samples to greedy energy minimization (part 1) / Author of the conference Pausinger, Florian.
- [Virtualconference] Billiard orbits and geodesics in non-integrable flat dynamical systems (part 1) / Author of the conference Chen, William.
- [Virtualconference] On the interplay between uniform distribution, discrepancy, and energy minimization / Author of the conference Bilyk, Dmitriy.
Bibliography
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