Asymptotic normality for random polytopes in non-Euclidean geometries

Florian Besau; Christoph Thäle

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arXiv · 1909.05607

Asymptotic normality for random polytopes in non-Euclidean geometries

Florian Besau·Christoph Thäle

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Abstract

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.

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Florian Besau, Christoph Thäle. 2019-09-12. Asymptotic normality for random polytopes in non-Euclidean geometries. https://arxiv.org/abs/1909.05607

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