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.
Publié le : 2007-07-14
Classification:
Random polytopes,
Gaussian distribution,
central limit theorem,
dependency graph,
60D05,
52A22,
60C05,
60F12
@article{1181334254,
author = {B\'ar\'any, Imre and Vu, Van},
title = {Central limit theorems for Gaussian polytopes},
journal = {Ann. Probab.},
volume = {35},
number = {1},
year = {2007},
pages = { 1593-1621},
language = {en},
url = {http://dml.mathdoc.fr/item/1181334254}
}
Bárány, Imre; Vu, Van. Central limit theorems for Gaussian polytopes. Ann. Probab., Tome 35 (2007) no. 1, pp. 1593-1621. http://gdmltest.u-ga.fr/item/1181334254/