On the variance of random polytopes |
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Authors: | Imre Bárány Matthias Reitzner |
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Institution: | Hungarian Academy of Sciences, Alfred Renyi Mathematical Institute, Budapest, Hungary |
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Abstract: | A random polytope is the convex hull of uniformly distributed random points in a convex body K. A general lower bound on the variance of the volume and f-vector of random polytopes is proved. Also an upper bound in the case when K is a polytope is given. For polytopes, as for smooth convex bodies, the upper and lower bounds are of the same order of magnitude. The results imply a law of large numbers for the volume and f-vector of random polytopes when K is a polytope. |
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Keywords: | Random polytopes Convex bodies Variance Floating body |
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