Limit theorems for random polytopes with vertices on convex surfaces
2018 ◽
Vol 50
(4)
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pp. 1227-1245
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Abstract We consider the random polytope Kn, defined as the convex hull of n points chosen independently and uniformly at random on the boundary of a smooth convex body in ℝd. We present both lower and upper variance bounds, a strong law of large numbers, and a central limit theorem for the intrinsic volumes of Kn. A normal approximation bound from Stein's method and estimates for surface bodies are among the tools involved.
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1974 ◽
Vol 11
(03)
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pp. 582-587
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1986 ◽
Vol 407
(1832)
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pp. 171-182
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2017 ◽
Vol 54
(2)
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pp. 569-587
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2019 ◽
pp. 1-19
2017 ◽
Vol 96
(2)
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pp. 333-344
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1969 ◽
Vol 136
◽
pp. 545
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