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Minimum separation among $m$ random points on an $n$-dimensional unit sphere

If the angle between the vectors $v_i$ and $v_j$ is denoted by $\theta_{ij}$, then using cosine rule we have $$\rho = 2 \min_{i,j \in\{1,2,\dots,m\}}\sin({\theta_{ij}}/{2})$$ Assuming that $m$ is a la …
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