The Annals of Probability

Poisson polytopes

Imre Bárány and Matthias Reitzner

Full-text: Open access

Abstract

We prove the central limit theorem for the volume and the f-vector of the Poisson random polytope Πη in a fixed convex polytope P ⊂ ℝd. Here, Πη is the convex hull of the intersection of a Poisson process X of intensity η with P.

Article information

Source
Ann. Probab., Volume 38, Number 4 (2010), 1507-1531.

Dates
First available in Project Euclid: 8 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1278593958

Digital Object Identifier
doi:10.1214/09-AOP514

Mathematical Reviews number (MathSciNet)
MR2663635

Zentralblatt MATH identifier
1204.60018

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 52A22: Random convex sets and integral geometry [See also 53C65, 60D05]
Secondary: 60C05: Combinatorial probability 60F15: Strong theorems

Keywords
Random polytopes CLT approximation of convex bodies dependency graph

Citation

Bárány, Imre; Reitzner, Matthias. Poisson polytopes. Ann. Probab. 38 (2010), no. 4, 1507--1531. doi:10.1214/09-AOP514. https://projecteuclid.org/euclid.aop/1278593958


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