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On a test for codes.

Falucskai, J. (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

On bilinear forms based on the resolvent of large random matrices

Walid Hachem, Philippe Loubaton, Jamal Najim, Pascal Vallet (2013)

Annales de l'I.H.P. Probabilités et statistiques

Consider a N × n non-centered matrix 𝛴 n with a separable variance profile: 𝛴 n = D n 1 / 2 X n D ˜ n 1 / 2 n + A n . Matrices D n and D ˜ n are non-negative deterministic diagonal, while matrix A n is deterministic, and X n is a random matrix with complex independent and identically distributed random variables, each with mean zero and variance one. Denote by Q n ( z ) the resolvent associated to 𝛴 n 𝛴 n * , i.e. Q n ( z ) = 𝛴 n 𝛴 n * - z I N - 1 . Given two sequences of deterministic vectors ( u n ) and ( v n ) with bounded Euclidean norms, we study the limiting behavior of the random bilinear form: u n * Q n ( z ) v n z - + , as the dimensions...

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