Sharp bounds on the rate of convergence of the empirical covariance matrix;Ordre asymptotique des valeurs singulières extrêmes de la matrice de covariance empirique

Comptes Rendus Mathematique

Volumn 349, Issue 3-4, 2011, Pages 195-200

  Adamczak, Radosław ^a   Litvak, Alexander E ^b   Pajor, Alain ^c   Tomczak Jaegermann, Nicole ^b  

^a UNIVERSITY OF WARSAW   (Poland)

^b UNIVERSITY OF ALBERTA   (Canada)

^c Projet Mathrisk INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79551492613     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2010.12.014     Document Type: Article

References (7)

1. Adamczak R., Litvak A.E., Pajor A., Tomczak-Jaegermann N. Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles. J. Amer. Math. Soc. 2010, 234:535-561.
2. Aubrun G. Random points in the unit ball of pn. Positivity 2006, 10:755-759.
3. Aubrun G. Sampling convex bodies: a random matrix approach. Proc. Amer. Math. Soc. 2007, 135:1293-1303.
4. Bai Z.D., Yin Y.Q. Limit of the smallest eigenvalue of a large dimensional sample covariance matrix. Ann. Probab. 1993, 21:1275-1294.
5. Kannan R., Lovász L., Simonovits M. Isoperimetric problems for convex bodies and a localization lemma. Discrete Comput. Geom. 1995, 13(3-4):541-559.
6. Kannan R., Lovász L., Simonovits M. Random walks and O(n5) volume algorithm for convex bodies. Random Structures Algorithms 1997, 2(1):1-50.
7. Paouris G. Concentration of mass on convex bodies. Geom. Funct. Anal. 2006, 16(5):1021-1049.