Low discrepancy sequences failing Poissonian pair correlations

DOI10.1007/S00013-019-01336-3zbMath1470.11207arXiv1903.02106OpenAlexW2963352283WikidataQ127954485 ScholiaQ127954485MaRDI QIDQ2311093

Verónica Becher, Olivier Carton, Ignacio Mollo Cunningham

Publication date: 10 July 2019

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.02106

zbMATH Keywords

low discrepancy sequencesdistribution modulo 1Poissonian pair correlationsBorel normal numbersnested perfect necklacesPascal triangle matrices

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) Irregularities of distribution, discrepancy (11K38)

Related Items (3)

Deviation from equidistance for one-dimensional sequences ⋮ The metric theory of the pair correlation function of real-valued lacunary sequences ⋮ Sequences with almost Poissonian pair correlations

Cites Work

• The pair correlation function of fractional parts of polynomials
• On extending de Bruijn sequences
• Normal numbers and nested perfect necklaces
• Some negative results related to Poissonian pair correlation problems
• Pair correlations and equidistribution
• On pair correlation and discrepancy
• The champernowne constant is not Poissonian
• On the discrepancy estimate of normal numbers
• A metric result on the pair correlation of fractional parts of sequences
• On absolute (j, ε)-normality in the rational fractions with applications to normal numbers
• The two-point correlation function of the fractional parts of $\sqrt {n}$ is Poisson
• An alternative construction of normal numbers
• The distribution of spacings between the fractional parts of \(n^2\alpha\)

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