HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

On bilinear forms based on the resolvent of large random matrices

Abstract : Consider a matrix $\Sigma_n$ with random independent entries, each non-centered with a separable variance profile. In this article, we study the limiting behavior of the random bilinear form $u_n^* Q_n(z) v_n$, where $u_n$ and $v_n$ are deterministic vectors, and Q_n(z) is the resolvent associated to $\Sigma_n \Sigma_n^*$ as the dimensions of matrix $\Sigma_n$ go to infinity at the same pace. Such quantities arise in the study of functionals of $\Sigma_n \Sigma_n^*$ which do not only depend on the eigenvalues of $\Sigma_n \Sigma_n^*$, and are pivotal in the study of problems related to non-centered Gram matrices such as central limit theorems, individual entries of the resolvent, and eigenvalue separation.
Document type :
Journal articles
Complete list of metadata

Contributor : Jamal Najim Connect in order to contact the contributor
Submitted on : Tuesday, August 23, 2011 - 1:25:06 PM
Last modification on : Saturday, January 15, 2022 - 3:56:43 AM
Long-term archiving on: : Friday, November 25, 2011 - 12:01:03 PM


Files produced by the author(s)



Walid Hachem, Philippe Loubaton, Jamal Najim, Pascal Vallet. On bilinear forms based on the resolvent of large random matrices. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2013, 49 (1), pp.36-63. ⟨10.1214/11-AIHP450⟩. ⟨hal-00474126v2⟩



Record views


Files downloads