Pair correlation and equidistribution on manifolds

DOI10.1007/s00605-019-01308-3zbMath1445.11074arXiv1903.00670OpenAlexW2918564152WikidataQ127663816 ScholiaQ127663816MaRDI QIDQ2291634

Jens Marklof

Publication date: 31 January 2020

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.00670

zbMATH Keywords

equidistributionpair correlationPoisson process

Mathematics Subject Classification ID

Probabilistic theory: distribution modulo (1); metric theory of algorithms (11K99) General theory of distribution modulo (1) (11K06) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (9)

Pair correlations of Halton and Niederreiter sequences are not Poissonian ⋮ Remarks about inhomogeneous pair correlations ⋮ On higher dimensional Poissonian pair correlation ⋮ Gap statistics and higher correlations for geometric progressions modulo one ⋮ A pair correlation problem, and counting lattice points with the zeta function ⋮ Poissonian correlation of higher order differences ⋮ On the number of gaps of sequences with Poissonian pair correlations ⋮ Some connections between discrepancy, finite gap properties, and pair correlations ⋮ Poissonian correlations of higher orders

Uses Software

• spatial

Cites Work

• The pair correlation function of fractional parts of polynomials
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• Some negative results related to Poissonian pair correlation problems
• Pair correlations and equidistribution
• On pair correlation and discrepancy
• Pair correlation for quadratic polynomials mod 1
• Pair correlation for fractional parts of αn²
• The $\bm{n}$-point correlations between values of a linear form
• ADDITIVE ENERGY AND THE METRIC POISSONIAN PROPERTY
• THE PRIMES ARE NOT METRIC POISSONIAN
• THERE IS NO KHINTCHINE THRESHOLD FOR METRIC PAIR CORRELATIONS
• The Distribution of Directions in an Affine Lattice: Two-Point Correlations and Mixed Moments
• The two-point correlation function of the fractional parts of $\sqrt {n}$ is Poisson
• Localized quantitative criteria for equidistribution
• Unnamed Item

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