Central Limit Theorems for Random Polytopes in a Smooth Convex Set
نویسنده
چکیده
Let K be a smooth convex set with volume one in R. Choose n random points in K independently according to the uniform distribution. The convex hull of these points, denoted by Kn, is called a random polytope. We prove that several key functionals of Kn satisfy the central limit theorem as n tends to infinity.
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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