Geodesic
Estimate of the distance between two bodies inside an $n$-dimensional unit cube and a ball
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2015), pp. 23-28 
F. A. Ivlev. Estimate of the distance between two bodies inside an $n$-dimensional unit cube and a ball. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2015), pp. 23-28. http://geodesic.mathdoc.fr/item/VMUMM_2015_6_a3/
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     title = {Estimate of the distance between two bodies inside an $n$-dimensional unit cube and a ball},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of estimation of the distance between two bodies of volume $\varepsilon$ located inside an $n$-dimensional body $B$ of unit volume where $n \to \infty$ is considered. In some cases such distances are bounded by a function of $\varepsilon$ not dependent on $n$. The cases when $B$ is a sphere or a cube are considered.

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