Central limit theorems for random polytopes
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- Reitzner, M. Probab. Theory Relat. Fields (2005) 133: 483. doi:10.1007/s00440-005-0441-8
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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.