O. Vlasiuk

activity

20162022

most citedAsymptotic properties of short-range interaction functionals

2 citations · 3 across the 3 of their papers we have counts for

collaborators

4 papers

math.CA2022

Asymptotics of $k$ -nearest neighbor Riesz energies

Douglas P. Hardin, Edward B. Saff, Oleksandr Vlasiuk

We obtain new asymptotic results about systems of $N$ particles governed by Riesz interactions involving $k$ -nearest neighbors of each particle as $N \to \infty$ . These results i…

math.CA2020★ 2 cited

Asymptotic properties of short-range interaction functionals

Douglas Hardin, Edward B. Saff, Oleksandr Vlasiuk

We describe a framework for extending the asymptotic behavior of a short-range interaction from the unit cube to general compact subsets of $R^{d}$ . This framework allows u…

math.CA2018

Riesz energy on self-similar sets

Alexander Reznikov, Oleksandr Vlasiuk

We investigate properties of minimal $N$ -point Riesz $s$ -energy on fractal sets of non-integer dimension, as well as asymptotic behavior of $N$ -point configurations that minimize t…

math.CA2016★ 1 cited

A minimum principle for potentials with application to Chebyshev constants

A. Reznikov, E. B. Saff, O. V. Vlasiuk

For "Riesz-like" kernels $K (x, y) = f (∣ x - y ∣)$ on $A \times A$ , where $A$ is a compact $d$ -regular set $A \subset R^{p}$ , we prove a minimum principle for potentials $U_K^μ=\int K…

Asymptotics of k-nearest neighbor Riesz energies

Asymptotic properties of short-range interaction functionals

Riesz energy on self-similar sets

A minimum principle for potentials with application to Chebyshev constants

Asymptotics of $k$ -nearest neighbor Riesz energies