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Abstract: Consider a matrix $\Sigma n$ with random independent entries, eachnon-centered with a separable variance profile. In this article, we study thelimiting behavior of the random bilinear form $u n^* Q nz v n$, where $u n$and $v n$ are deterministic vectors, and Q nz is the resolvent associated to$\Sigma n \Sigma n^*$ as the dimensions of matrix $\Sigma n$ go to infinity atthe 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-centeredGram matrices such as central limit theorems, individual entries of theresolvent, and eigenvalue separation.



Author: Walid Hachem LTCI, Philippe Loubaton LIGM, Jamal Najim LTCI, Pascal Vallet IGM

Source: https://arxiv.org/







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