Virtualconference
H On two different topics in discrepancy theory: From the discrepancy of stratified samples to greedy energy minimization (part 1)
Auteurs : Pausinger, Florian (Auteur de la Conférence)
CIRM (Editeur )
CIRM (Editeur )
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Greedy energy minimization and the van der Corput sequence (part 3)
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Discrepancy of stratified samples from partitions of the unit cube (part 2)
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- 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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Résumé :
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.
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
Codes MSC :
11K31
- Special sequences
11K38
- Irregularities of distribution, discrepancy
52C25
- Rigidity and flexibility of structures, See also {70B15}
Ressources complémentaires :
https://www.cirm-math.com/uploads/2/6/6/0/26605521/pausinger_part1.pdf
Florian Pausinger: Discrepancy of stratified samples from partitions of the unit cube (part 2)
Florian Pausinger: Greedy energy minimization and the van der Corput sequence (part 3)
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 30/11/2020 Date de captation : 30/11/2020 Collection : Research talks ; Number Theory ; Mathematical Physics ; Probability and Statistics Durée : 00:16:23 Domaine : Number Theory ; Probability & Statistics ; Mathematical Physics Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2020-11-19_Pausinger 1.mp4 
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Informations sur la Rencontre Virtuelle
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
Citation Data
DOI : 10.24350/CIRM.V.19681703Cite this video as: Pausinger, Florian (2020). On two different topics in discrepancy theory: From the discrepancy of stratified samples to greedy energy minimization (part 1).CIRM . Audiovisual resource. doi:10.24350/CIRM.V.19681703 URI : http://dx.doi.org/10.24350/CIRM.V.19681703 |
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