Abstract:
The Tarasov–Zaporozhets conjecture is considered, which states that the mean distance between two random points nside a convex body does not exceed the mean distance between points on its boundary. The main result of this work is a proof of this conjecture for centrally symmetric planar bodies. It is also established that for sufficiently high moments, an analogous inequality holds for any convex body of arbitrary dimension.
Key words and phrases:convex bodies, geometric probability, mean distance, random points, central symmetry, stochastic majorization, isoperimetric inequality, random sections, integral geometry.
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