Abstract
Let K be a smooth convex set. The convex hull of independent random points in K is a random polytope. Central limit theorems for the volume and the number of i dimensional faces of random polytopes are proved as the number of random points tends to infinity. One essential step is to determine the precise asymptotic order of the occurring variances.
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Research was supported in part by the European Network PHD, MCRN-511953.
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Reitzner, M. Central limit theorems for random polytopes. Probab. Theory Relat. Fields 133, 483–507 (2005). https://doi.org/10.1007/s00440-005-0441-8
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DOI: https://doi.org/10.1007/s00440-005-0441-8