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Mean minimum distance for K random points on a N-dimensional (hyper-)cube

The following paper: Bhattacharyya, P., and B. K. Chakrabarti. The mean distance to the nth neighbour in a uniform distribution of random points: an application of probability theory. Eur J. Phys. 29 …
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The consequence of overlap sharing for the length-distribution of rods randomly placed on a ...

Please imagine that one populates a finite line of unit length, or circle with unit length contour (to avoid edge-effects), with $N$ one-dimensional 'rods' such that their LHS-ends, at positions $(p_1 …