Premium
Irregularities of distributions with respect to polytopes
Author(s) -
Drmota Michael
Publication year - 1996
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s002557930001161x
Subject(s) - mathematics , homothetic transformation , polytope , generalization , combinatorics , regular polygon , simple (philosophy) , order (exchange) , torus , point (geometry) , convex body , mathematical analysis , geometry , convex optimization , philosophy , epistemology , finance , economics
In the first part of the paper we show that the L 2 ‐discrepancy with respect to squares is of the same order of magnitude as the usual L 2 ‐ discrepancy for point distributions in the K ‐dimensional torus. In the second part we adapt this method to obtain a generalization of Roth's [7] lower bound (log N ) ( k ‐1)/2 (for the usual discrepancy) to the discrepancy with respect to homothetic simple convex poly topes.