Discrepancy of point sequences on fractal sets

Details

Ressource 1Download: BIB_3390FCE28A61.P001.pdf (326.86 [Ko])
State: Public
Version: author
Serval ID
serval:BIB_3390FCE28A61
Type
Article: article from journal or magazin.
Collection
Publications
Title
Discrepancy of point sequences on fractal sets
Journal
Publicationes Mathematicae Debrecen
Author(s)
Albrecher H., Matousek J., Tichy R.
ISSN
0033-3883
Publication state
Published
Issued date
2000
Peer-reviewed
Oui
Volume
56
Number
3-4
Pages
233-249
Language
english
Abstract
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.
Keywords
Discrepancy, Fractals, Halfspaces
Web of science
Create date
12/05/2009 11:06
Last modification date
20/08/2019 13:19
Usage data