Phase transition for the volume of high‐dimensional random polytopes
نویسندگان
چکیده
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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 Nati...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2020
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20986