discrepancy
discrepancy of generalized Zaremba point sets
We give an exact formula for the discrepancy of a class of generalized two-dimensional Hammersley point sets in base , namely generalized Zaremba point sets. These point sets are digitally shifted Hammersley point sets with an arbitrary number of different digital shifts in base . The Zaremba point set introduced by White in 1975 is the special case where the shifts are taken repeatedly in sequential order, hence needing at least points to obtain the optimal order of discrepancy. On the...
- and -discrepancy of (order 2) digital nets
Dick proved that all dyadic order 2 digital nets satisfy optimal upper bounds on the -discrepancy. We prove this for arbitrary prime base b with an alternative technique using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds on the discrepancy function in Besov spaces with dominating mixed smoothness for a certain parameter range, and enlarge that range for order 2 digital nets. The discrepancy function in Triebel-Lizorkin and Sobolev spaces with dominating mixed...
-discrepancy and statistical independence of sequences
We characterize statistical independence of sequences by the -discrepancy and the Wiener -discrepancy. Furthermore, we find asymptotic information on the distribution of the -discrepancy of sequences.
L₂ discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations
La répartition modulo 1 des puis-sances de rationnels dans l'anneau des séries formelles sur un corps fini
Les ensembles de Bésineau
Les ensembles de van der Corput
Les suites à spectre vide et la répartition modulo
Les suites additives et leur répartition (mod.1)
Limit theorems for lacunary series and uniform distribution mod 1
Limit theorems for uniformly distributed p-adic sequences
Lineare Gleichverteilung.
Lineare Gleichverteilung.
Low-Discrepancy Point Sets.
Low-discrepancy sequences obtained from algebraic function fields over finite fields