5 citations · 8 across the 8 of their papers we have counts for
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math.NT2019
Poissonian pair correlation on manifolds via the heat kernel
Peter J. Grabner, Tetiana A. Stepanyuk
We define a notion of Poissonian pair correlation (PPC) for Riemannian manifolds without boundary and prove that PPC implies uniform distribution in this setting. This extends earl…
math.CA2019
Hyperuniform point sets on flat tori: deterministic and probabilistic aspects
Tetiana Stepanyuk
In this paper we study hyperuniformity on flat tori. Hyperuniform point sets on the unit sphere have been studied by J.~Brauchart, P.~Grabner, W.~Kusner and J.~Ziefle. It is shown…
math.CA2019
Estimates for logarithmic and Riesz energies for spherical -designs
Tetiana Stepanyuk
In this paper we find asymptotic equalities for the discrete logarithmic energy of sequences of well separated spherical -designs on the unit sphere ${\mathbb{S}^{d}\subset\math…