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 convergence presque sûre des moyennes ergodiques suivant certaines sous-suites d'entiers
La mesure des ensembles non-normaux.
La répartition modulo de la suite et les ensembles de Cantor
La répartition modulo 1 des puis-sances de rationnels dans l'anneau des séries formelles sur un corps fini
Large deviations of sums of independent random variables
Large families of elliptic curve pseudorandom binary sequences
Large families of pseudorandom binary sequences and lattices by using the multiplicative inverse
Large families of pseudorandom binary sequences and lattices are constructed by using the multiplicative inverse and estimates of exponential sums in a finite field. Pseudorandom measures of binary sequences and lattices are studied.
Large families of pseudorandom binary sequences constructed by using the Legendre symbol
Le théorème ergodique le long d’une suite -multiplicative
Les ensembles de Bésineau
Les ensembles de van der Corput
Les nombres de Pisot et la synthèse spectrale
Les suites à spectre vide et la répartition modulo
Les suites additives et leur répartition (mod.1)
Les suites eutaxiques