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Discrepancy of stratified samples from partitions of the unit cube (part 2)
Virtualconference
Authors : Pausinger, Florian (Author of the conference)
CIRM (Publisher )
11K31 - Special sequences
11K38 - Irregularities of distribution, discrepancy
52C25 - Rigidity and flexibility of structures, See also {70B15}
Additional resources :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/pausinger_part2.pdf
CIRM (Publisher )
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Abstract :
In this talk I will report on recent progress on two different problems in discrepancy theory. In the first part I will present a recent extension of the notion of jittered sampling to arbitrary partitions of the unit cube. In this joint work with Markus Kiderlen from Aarhus, we introduce the notion of a uniformly distributed triangular array. Moreover, we show that the expected Lp-discrepancy of a point sample generated from an arbitrary equi volume partition of the unit cube is always strictly smaller than the expected Lp-discrepancy of a set of N uniform random samples for p > 1.
The second part of the talk is dedicated to greedy energy minimization. I will give a new characterisation of the classical van der Corput sequence in terms of a minimization problem and will discuss various related open questions.
Keywords : discrepancy theory; jittered sampling; stratified sampling; energy minimization
MSC Codes : The second part of the talk is dedicated to greedy energy minimization. I will give a new characterisation of the classical van der Corput sequence in terms of a minimization problem and will discuss various related open questions.
Keywords : discrepancy theory; jittered sampling; stratified sampling; energy minimization
11K31 - Special sequences
11K38 - Irregularities of distribution, discrepancy
52C25 - Rigidity and flexibility of structures, See also {70B15}
Additional resources :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/pausinger_part2.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 30/11/2020 Conference Date : 30/11/2020 Subseries : Research talks arXiv category : Mathematical Physics ; Classical Analysis and ODEs ; Number Theory Mathematical Area(s) : Number Theory ; Mathematical Physics ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:25:46 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-19_Pausinger_2.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.19691603Cite this video as: Pausinger, Florian (2020). Discrepancy of stratified samples from partitions of the unit cube (part 2). CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19691603 URI : http://dx.doi.org/10.24350/CIRM.V.19691603 |
See Also
- [Virtualconference] Greedy energy minimization and the van der Corput sequence (part 3) / 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.
- [Virtualconference] Local and global statistics for point sequences / Author of the conference Aistleitner, Christoph.
Bibliography
- KIDERLEN, Markus et PAUSINGER, Florian. Discrepancy of stratified samples from partitions of the unit cube. arXiv preprint arXiv:2008.12026, 2020. - https://arxiv.org/abs/2008.12026
- PAUSINGER, Florian. Greedy energy minimization can count in binary: point charges and the van der Corput sequence. arXiv preprint arXiv:1905.09641, 2019. To appear, Ann. Math. Pura. Appl. - https://arxiv.org/abs/1905.09641
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