Year: 2008
Type: article
Abstract: In our paper [1], we prove the central limit theorem for the number of j -dimensional faces, f j (K n ), j = 0, 1, . . ., d -1, and for the volume, Vol(K n ), of the Gaussian random polytope K n .Here, K n is just the convex hull of n random and independent Gaussian vectors from R d .There is a nonmathematical (and very unfortunate) error on page 1595 of the paper.There, we say that Irene Hueter's proof of the central limit theorem for f 0 (K n ) in [2] and [3] contains a gap.This statement is false-her proof is correct.Our error is due to an unfortunate misunderstanding and the mixing up of two results from [2] and [3]; see also comments in [4].So, besides apologies, this correction note is also an acknowledgment of priority: the first proof of the central limit theorem for f 0 (K n ), the number of vertices of the Gaussian random polytope, is due to Hueter in [3].
Source: The Annals of Probability
DOI: 10.1214/07-aop378
Authors: Imre Bárány, Van Vu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2949644757