Asymptotics for Discrete Weighted Minimal Riesz Energy Problems on Rectifiable Sets
نویسنده
چکیده
Given a compact d-rectifiable set A embedded in Euclidean space and a distribution ρ(x) with respect to d-dimensional Hausdorff measure on A, we address the following question: how can one generate optimal configurations of N points on A that are “well-separated” and have asymptotic distribution ρ(x) as N → ∞? For this purpose we investigate minimal weighted Riesz energy points, that is, points interacting via the weighted power law potential V = w(x, y) |x− y|, where s > 0 is a fixed parameter and w is suitably chosen. In the unweighted case (w ≡ 1) such points for N fixed tend to the solution of the best-packing problem on A as the parameter s → ∞.
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