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Random Sections of Convex Bodies

Consider a convex body D in ℝn. We obtain an explicit formula expressing the distribution function of the distance between two random points uniformly and independently chosen in D in terms of the distribution function of the length of a random chord of D. As a corollary, we derive Kingman’s formula which connects the moments of these distributions.

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Correspondence to T. Moseeva.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 486, 2019, pp. 190–199.

Translated by by T. Moseeva.

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Moseeva, T. Random Sections of Convex Bodies. J Math Sci 258, 867–872 (2021).

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