Hyperuniform point sets on the sphere: probabilistic aspects

Brauchart, Johann S.; Grabner, Peter J.; Kusner, Wöden; Ziefle, Jonas

doi:10.1007/s00605-020-01439-y

Cited by 16 publications

(13 citation statements)

References 15 publications

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“…Theorem 2.2 is given here to compare it with Theorem 2.3 below. Notice also that the upper bound (7) is better than (8) with p = 2 and G = G 1 by a logarithmic factor. Such an improvement is obtained in [1] because of the explicit formula (6) for the quadratic discrepancy with the uniform weights G 1 .…”

Section: Be a Finite Collection Of Real-valued Independent Random Var...mentioning

confidence: 93%

Bounds for discrepancies in the Hamming space

Barg¹,

Skriganov²

2020

Preprint

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We derive bounds for the ball Lp-discrepancies in the Hamming space for 0 < p < ∞ and p = ∞. Sharp estimates of discrepancies have been obtained for many spaces such as the Euclidean spheres and more general compact Riemannian manifolds. In the present paper, we show that the behavior of discrepancies in the Hamming space differs fundamentally because the volume of the ball in this space depends on its radius exponentially while such a dependence for the Riemannian manifolds is polynomial.

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Section: Be a Finite Collection Of Real-valued Independent Random Var...mentioning

confidence: 93%

Bounds for discrepancies in the Hamming space

Barg¹,

Skriganov²

2020

Preprint

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show abstract

“…The jittered sampling point process is also a DPP with kernel [13]. Here, we omit the expression of the 2-point correlation because we use the same methods as in Brauchart et al [2] in the proof of Theorem 10.…”

Section: Definitionmentioning

confidence: 99%

On $p$-frame potentials of determinantal point processes on the sphere

Hirao

2021

JSIAM Letters

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“…Here f is some potential depending only on the distance of two points. In many cases these computations lead to integrals of the form (1) (see [1,3,4,6]).…”

Section: Integrals Of the Formmentioning

confidence: 99%