D. Bilyk

collaborators

4 papers

math.CA2026

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 $s$ -Riesz and Green energy sequences ${x_{n}}_{n = 1}^{\infty}$ on the unit sphere $S^{d} \subset R^{d + 1}$ , where…

math.MG2025

Minimizing point configurations for tensor product energies on the torus

Dmitriy Bilyk, Nicolas Nagel, Ian Ruohoniemi

We study point configurations on the torus $T^{d}$ that minimize interaction energies with tensor product structure which arise naturally in the context of discrepancy theory…

math.CA2025

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 $L_{2}$ -discrepancy of any $N$ points…

math.PR2025

Regularizing random points by deleting a few

Dmitriy Bilyk, Stefan Steinerberger

It is well understood that if one is given a set $X \subset [0, 1]$ of $n$ independent uniformly distributed random variables, then $$ \sup_{0 \leq x \leq 1} \left| \frac{\# X \cap…