Deterministic Equivalents for Certain Functionals of Large Random Matrices
نویسنده
چکیده
Abstract. Consider a N × n random matrix Yn = (Y n ij ) where the entries are given by Y n 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 for the Euclidean norm. Let Σn = 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 surely,
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