A Rate of Convergence Result for the Largest Eigenvalue of Complex White Wishart Matrices

@inproceedings{Karoui2006ARO,
  title={A Rate of Convergence Result for the Largest Eigenvalue of Complex White Wishart Matrices},
  author={Noureddine El Karoui},
  year={2006}
}
It has been recently shown that if X is an n × N matrix whose entries are i.i.d. standard complex Gaussian and l1 is the largest eigenvalue of X∗X, there exist sequences mn,N and sn,N such that (l1 − mn,N )/sn,N converges in distribution to W2, the Tracy–Widom law appearing in the study of the Gaussian unitary ensemble. This probability law has a density which is known and computable. The cumulative distribution function of W2 is denoted F2. In this paper we show that, under the assumption that… CONTINUE READING
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