97 citations · 463 across the 68 of their papers we have counts for
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Random Point Sets on the Sphere --- Hole Radii, Covering, and Separation
Johann S. Brauchart, Alexander B. Reznikov, Edward B. Saff +3
Geometric properties of random points distributed independently and uniformly on the unit sphere with respect to surface area measure ar…
Next order energy asymptotics for Riesz potentials on flat tori
Douglas P. Hardin, Edward B. Saff, Brian Z. Simanek +1
Let be a lattice in with positive co-volume. Among -periodic -point configurations, we consider the minimal renormalized Riesz -energy $\mathcal{E}_{s,Λ}(N…
Energy bounds for codes and designs in Hamming spaces
Peter G. Boyvalenkov, Peter D. Dragnev, Douglas P. Hardin +2
We obtain universal bounds on the energy of codes and for designs in Hamming spaces. Our bounds hold for a large class of potential functions, allow unified treatment, and can be v…
Universal upper and lower bounds on energy of spherical designs
P. G. Boyvalenkov, P. D. Dragnev, D. P. Hardin +2
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are vali…
Minimum Riesz energy problems for a condenser with "touching plates"
P. D. Dragnev, D. Hardin, E. B. Saff +1
Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solva…
The covering radius of randomly distributed points on a manifold
A. Reznikov, E. B. Saff
We derive fundamental asymptotic results for the expected covering radius for points that are randomly and independently distributed with respect to surface measure on…