Random polytopes
نویسنده
چکیده
We prove the central limit theorem for the volume and the f -vector of the random polytope Pn and the Poisson random polytope Πn in a fixed convex polytope P ⊂ IR. Here Pn is the convex hull of n random points in P , and Πn is the convex hull of the intersection of a Poisson process X(n), of intensity n, with P . A general lower bound on the variance is also proved. ∗Supported by Hungarian National Foundation Grants T 046246 and T 037846. †Research of both authors was supported in part by the European Network PHD, MCRN511953. AMS 2000 subject classifications. Primary 60D05; secondary 52A22, 60C05, 60F15.
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