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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L. Santaló, Integral Geometry and Geometric Probability, Addison–Wesley Publ. Company (1976).
R. Schneider and W. Weil, Stochastic and Integral Geometry, Springer Verlag (2008).
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). https://doi.org/10.1007/s10958-021-05585-y