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Stochastical approximation of smooth convex bodies
Author(s) -
Reitzner Matthias
Publication year - 2004
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015473
Subject(s) - mathematics , convex hull , polytope , convex body , convex polytope , boundary (topology) , combinatorics , regular polygon , mixed volume , differentiable function , subderivative , class (philosophy) , convex combination , convex analysis , convex set , pure mathematics , mathematical analysis , geometry , convex optimization , artificial intelligence , computer science
A random polytope is the convex hull of n random points in the interior of a convex body K . The expectation of the i th intrinsic volume of a random polytope as n → ∞ is investigated. It is proved that, for convex bodies of differentiability class K k +1 , precise asymptotic expansions for these expectations exist. The proof makes essential use of a refinement of Crofton's boundary theorem.
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