Skip to Main content Skip to Navigation
Journal articles

Smallest singular value of random matrices and geometry of random polytopes

Abstract : We study the behaviour of the smallest singular value of a rectangular random matrix, i.e., matrix whose entries are independent random variables satisfying some additional conditions. We prove a deviation inequality and show that such a matrix is a "good" isomorphism on its image. Then, we obtain asymptotically sharp estimates for volumes and other geometric parameters of random polytopes (absolutely convex hulls of rows of random matrices). All our results hold with high probability, that is, with probability exponentially (in dimension) close to 1. (c) 2004 Elsevier Inc. All rights reserved.
Document type :
Journal articles
Complete list of metadatas

https://hal-upec-upem.archives-ouvertes.fr/hal-00693800
Contributor : Admin Lama <>
Submitted on : Wednesday, May 2, 2012 - 11:50:20 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

Identifiers

Citation

Ae Litvak, Alain Pajor, M Rudelson, N Tomczak-Jaegermann. Smallest singular value of random matrices and geometry of random polytopes. Advances in Mathematics, Elsevier, 2005, 195 (2), pp.491--523. ⟨10.1016/j.aim.2004.08.004⟩. ⟨hal-00693800⟩

Share

Metrics

Record views

2112