The Empirical Eigenvalue Distribution of a Gram Matrix : from Independence to Stationarity

@inproceedings{Najim2005TheEE,
  title={The Empirical Eigenvalue Distribution of a Gram Matrix : from Independence to Stationarity},
  author={Jamal Najim},
  year={2005}
}
Consider a N × n matrix Zn = (Zn j1j2 ) where the individual entries are a realization of a properly rescaled stationary gaussian random field: Z j1j2 = 1 √ n ∑ (k1,k2)∈Z2 h(k1, k2)U(j1 − k1, j2 − k2), where h ∈ `1(Z2) is a deterministic complex summable sequence and (U(j1, j2); (j1, j2) ∈ Z2) is a sequence of independent complex gaussian random variables with mean zero and unit variance. The purpose of this article is to study the limiting empirical distribution of the eigenvalues of Gram… CONTINUE READING
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