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arXiv:1909.05607 [math.PR]AbstractReferencesReviewsResources

Asymptotic normality for random polytopes in non-Euclidean geometries

Florian Besau, Christoph Thäle

Published 2019-09-12Version 1

Asymptotic normality for the natural volume measure of random polytopes generated by random points distributed uniformly in a convex body in spherical or hyperbolic spaces is proved. Also the case of Hilbert geometries is treated and central limit theorems in Lutwak's dual Brunn--Minkowski theory are established. The results follow from a central limit theorem for weighted random polytopes in Euclidean spaces. In the background are Stein's method for normal approximation and geometric properties of weighted floating bodies.

Comments: 7 figures
Categories: math.PR, math.MG
Subjects: 52A22, 52A55, 60D05, 60F05
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