Abstract
A random polytopeP n in a convex bodyC is the convex hull ofn identically and independently distributed points inC. Its expectation is a convex body in the interior ofC. We study the deviation of the expectation ofP n fromC asn→∞: while forC of classC k+1,k≥1, precise asymptotic expansions for the deviation exist, the behaviour of the deviation is extremely irregular for most convex bodiesC of classC 1.
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Dedicated to my teacher and friend Professor Edmund Hlawka on the occasion of his 80th birthday
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Gruber, P.M. Expectation of random polytopes. Manuscripta Math 91, 393–419 (1996). https://doi.org/10.1007/BF02567963
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DOI: https://doi.org/10.1007/BF02567963