Jean-Morlet Chair 2020 - Workshop: Discrepancy Theory and Applications - Part 1 / Chaire Jean-Morlet 2020 - Workshop : Théorie de la discrépance et applications - Part 1

Collection Jean-Morlet Chair 2020 - Workshop: Discrepancy Theory and Applications - Part 1 / Chaire Jean-Morlet 2020 - Workshop : Théorie de la discrépance et applications - Part 1

Organizer(s) Madritsch, Manfred ; Rivat, Joël ; Tichy, Robert

Date(s) 30/11/2020 - 01/12/2020

linked URL https://www.cirm-math.com/2257virtual.html

00:00:00 / 00:00:00

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Discrepancy of stratified samples from partitions of the unit cube (part 2)

By Florian Pausinger

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.

Information about the video

Date of recording 30/11/2020
Date of publication 30/11/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19691603
Cite this video Pausinger, Florian (30/11/2020). Discrepancy of stratified samples from partitions of the unit cube (part 2). CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19691603
URL https://dx.doi.org/10.24350/CIRM.V.19691603

Domain(s)

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

MSC codes

Document(s)

https://www.cirm-math.com/uploads/2/6/6/0/26605521/pausinger_part2.pdf

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