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The Diamond ensemble: a constructive set of spherical points with small logarithmic energy. (English) Zbl 1443.31004
Summary: We define a family of random sets of points, the Diamond ensemble, on the sphere \(\mathbb{S}^2\) depending on several parameters. Its most important property is that, for some of these parameters, the asymptotic expected value of the logarithmic energy of the points can be computed rigorously and shown to attain very small values, quite close to the conjectured minimal value.

MSC:
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
Software:
Maxima
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