For large N the optimal dispersed subset consists of all points lying outside a self-consistently determined d-dimensional ball, with the entire distribution of maximal dispersion obtained via mean-field order statistics and the replica method.
Ghildiyal et al.,Genomic insights into the conservation of wild and domestic animal diversity: A review, Gene886, 147719 (2023)
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The Most Dispersed Subset of Random Points in $\mathbb{R}^d$
For large N the optimal dispersed subset consists of all points lying outside a self-consistently determined d-dimensional ball, with the entire distribution of maximal dispersion obtained via mean-field order statistics and the replica method.