Let be independent centered random vectors with log-concave distribution and with the identity as covariance matrix. We show that with overwhelming probability one has
Soient des vecteurs aléatoires indépendants centrés, de matrice de covariance l'identité et à densité log-concave. On démontre qu'avec une grande probabilité, on a
Accepted:
Published online:
Radosław Adamczak 1; Alexander E. Litvak 2; Alain Pajor 3; Nicole Tomczak-Jaegermann 2
@article{CRMATH_2011__349_3-4_195_0, author = {Rados{\l}aw Adamczak and Alexander E. Litvak and Alain Pajor and Nicole Tomczak-Jaegermann}, title = {Sharp bounds on the rate of convergence of the empirical covariance matrix}, journal = {Comptes Rendus. Math\'ematique}, pages = {195--200}, publisher = {Elsevier}, volume = {349}, number = {3-4}, year = {2011}, doi = {10.1016/j.crma.2010.12.014}, language = {en}, }
TY - JOUR AU - Radosław Adamczak AU - Alexander E. Litvak AU - Alain Pajor AU - Nicole Tomczak-Jaegermann TI - Sharp bounds on the rate of convergence of the empirical covariance matrix JO - Comptes Rendus. Mathématique PY - 2011 SP - 195 EP - 200 VL - 349 IS - 3-4 PB - Elsevier DO - 10.1016/j.crma.2010.12.014 LA - en ID - CRMATH_2011__349_3-4_195_0 ER -
%0 Journal Article %A Radosław Adamczak %A Alexander E. Litvak %A Alain Pajor %A Nicole Tomczak-Jaegermann %T Sharp bounds on the rate of convergence of the empirical covariance matrix %J Comptes Rendus. Mathématique %D 2011 %P 195-200 %V 349 %N 3-4 %I Elsevier %R 10.1016/j.crma.2010.12.014 %G en %F CRMATH_2011__349_3-4_195_0
Radosław Adamczak; Alexander E. Litvak; Alain Pajor; Nicole Tomczak-Jaegermann. Sharp bounds on the rate of convergence of the empirical covariance matrix. Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 195-200. doi : 10.1016/j.crma.2010.12.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.12.014/
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☆ The research was conducted while the authors participated in the Thematic Program on Asymptotic Geometric Analysis at the Fields Institute in Toronto in Fall 2010.
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