14 citations · 88 across the 28 of their papers we have counts for
34 papers
Energy, Polarization, and Separation of Greedy Sequences for Riesz and Green Kernels
Dmitriy Bilyk, Liudmyla Kryvonos, Ryan W. Matzke +1
We investigate the asymptotic behavior of greedy -Riesz and Green energy sequences on the unit sphere , where…
Minimizing point configurations for tensor product energies on the torus
Dmitriy Bilyk, Nicolas Nagel, Ian Ruohoniemi
We study point configurations on the torus that minimize interaction energies with tensor product structure which arise naturally in the context of discrepancy theory…
On the lower bounds for the spherical cap discrepancy
Dmitriy Bilyk, Johann S. Brauchart
We start by providing a very simple and elementary new proof of the classical bound due to J. Beck which states that the spherical cap -discrepancy of any points…
Regularizing random points by deleting a few
Dmitriy Bilyk, Stefan Steinerberger
It is well understood that if one is given a set of independent uniformly distributed random variables, then $$ \sup_{0 \leq x \leq 1} \left| \frac{\# X \cap…
Positive definite singular kernels on two-point homogeneous spaces
Dmitriy Bilyk, Peter Grabner
We study positive definiteness of kernels on two-point homogeneous spaces. As opposed to the classical case, which has been developed and studied in the existing literatur…
Geodesic Distance Riesz Energy on Projective Spaces
Dmitriy Bilyk, Ryan W. Matzke, Joel Nathe
We study probability measures that minimize the Riesz energy with respect to the geodesic distance on projective spaces (such energies arise from…