Deterministic Equivalents for Certain Functionals of Large Random Matrices

@inproceedings{Hachem2007DeterministicEF,
  title={Deterministic Equivalents for Certain Functionals of Large Random Matrices},
  author={Walid Hachem and Philippe Loubaton and Jamal Najim},
  year={2007}
}
Consider an N ×n random matrix Yn = (Y n ij ) where the entries are given by Y ij = σij (n) √ n X ij , the X n ij being independent and identically distributed, centered with unit variance and satisfying some mild moment assumption. Consider now a deterministic N × n matrix An whose columns and rows are uniformly bounded in the Euclidean norm. Let n = Yn + An. We prove in this article that there exists a deterministic N × N matrix-valued function Tn(z) analytic in C − R+ such that, almost… CONTINUE READING
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