Discrepancy of point sequences on fractal sets

Détails

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Etat: Public
Version: de l'auteur
ID Serval
serval:BIB_3390FCE28A61
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Titre
Discrepancy of point sequences on fractal sets
Périodique
Publicationes Mathematicae Debrecen
Auteur(s)
Albrecher H., Matousek J., Tichy R.
ISSN
0033-3883
Statut éditorial
Publié
Date de publication
2000
Peer-reviewed
Oui
Volume
56
Numéro
3-4
Pages
233-249
Langue
anglais
Résumé
We consider asymptotic bounds for the discrepancy of point sets on a class of fractal sets. By a method of R. Alexander, we prove that for a wide class of fractals, the L-2-discrepancy (and consequently also the worst-case discrepancy) of an N-point set with respect to halfspaces is at least of the order N-1/2-1/2s, where s is the Hausdorff dimension of the fractal. We also show that for many fractals, this bound is tight for the L-2-discrepancy. Determining the correct order of magnitude of the worst-case discrepancy remains a challenging open problem.
Mots-clé
Discrepancy, Fractals, Halfspaces
Web of science
Création de la notice
12/05/2009 12:06
Dernière modification de la notice
20/08/2019 14:19
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