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July 2007 Central limit theorems for Gaussian polytopes
Imre Bárány, Van Vu
Ann. Probab. 35(4): 1593-1621 (July 2007). DOI: 10.1214/009117906000000791


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.


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Imre Bárány. Van Vu. "Central limit theorems for Gaussian polytopes." Ann. Probab. 35 (4) 1593 - 1621, July 2007.


Published: July 2007
First available in Project Euclid: 8 June 2007

zbMATH: 1124.60014
MathSciNet: MR2330981
Digital Object Identifier: 10.1214/009117906000000791

Primary: 60D05
Secondary: 52A22 , 60C05 , 60F12

Keywords: central limit theorem , dependency graph , Gaussian distribution , Random polytopes

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 4 • July 2007
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