On the distance distribution between random points in a hypercube

In this work the distance distribution function between random points in a hypercube is investigated. The exact formula for the distance distribution function in the region $r < 1$ is obtained. Calculations have been performed to refine the asymptotics of the distance distribution function in the region $r < 1$ for large distances. It is shown that this probability decreases faster than its qualitative assessment by the volume of an $n$-dimensional sphere. The results of numerical simulation of the distribution of distances in a large-dimensional hypercube are presented. The asymptotic of the distance distribution function is obtained.