Mathematical analysis reveals distance distributions between random points in spherical shells and beta models, suggesting new insights for geometry.
We study the distribution of the distance of a pair of independent random points selected uniformly in concentric spherical shells in R d .Additionally, we rederive the distribution of the distance between two random points in a ball selected according to the beta distribution.Finally, we also consider the distance between two points following a beta distribution in a concentric spherical shell in some special cases for and d.
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Bakó‐Szabó et al. (2026) studied this question.
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