The Annals of Probability

Central limit theorems for Gaussian polytopes

Imre Bárány and Van Vu

Full-text: Open access

Abstract

Choose n random, independent points in Rd according to the standard normal distribution. Their convex hull Kn is the Gaussian random polytope. We prove that the volume and the number of faces of Kn satisfy the central limit theorem, settling a well-known conjecture in the field.

Article information

Source
Ann. Probab. Volume 35, Number 4 (2007), 1593-1621.

Dates
First available in Project Euclid: 8 June 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1181334254

Digital Object Identifier
doi:10.1214/009117906000000791

Mathematical Reviews number (MathSciNet)
MR2330981

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 52A22: Random convex sets and integral geometry [See also 53C65, 60D05] 60C05: Combinatorial probability 60F12

Keywords
Random polytopes Gaussian distribution central limit theorem dependency graph

Citation

Bárány, Imre; Vu, Van. Central limit theorems for Gaussian polytopes. Ann. Probab. 35 (2007), no. 4, 1593--1621. doi:10.1214/009117906000000791. http://projecteuclid.org/euclid.aop/1181334254.


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