July 2007
Central limit theorems for Gaussian polytopes
Imre Bárány, Van Vu
Ann. Probab. 35(4): 1593-1621 (July 2007). DOI: 10.1214/009117906000000791
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.
Citation
Download CitationImre Bárány. Van Vu. "Central limit theorems for Gaussian polytopes." Ann. Probab. 35 (4) 1593 - 1621, July 2007. https://doi.org/10.1214/009117906000000791
Information
Published: July 2007
First available in Project Euclid: 8 June 2007
Digital Object Identifier: 10.1214/009117906000000791
Subjects:
Primary: 60D05
Secondary: 52A22 , 60C05 , 60F12
Keywords: central limit theorem , dependency graph , Gaussian distribution , Random polytopes
Rights: Copyright © 2007 Institute of Mathematical Statistics
JOURNAL ARTICLE
29 PAGES
Vol.35 • No. 4 • July 2007
