Central Limit Theorems for Gaussian Polytopes
نویسنده
چکیده
Choose n random, independent points in R according to the standard normal distribution. Their convex hull Kn is the Gaussian random polytope. We prove that the volume and the number of faces of Kn satisfy the central limit theorem, settling a well known conjecture in the field.
منابع مشابه
Central Limit Theorems for Random Polytopes
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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تاریخ انتشار 2006