Universality in Complex Wishart ensembles: The 2 cut case

We studied the universality of Wishart ensembles whose covariance matrix has 2 distinct eigenvalues. We studied the asymptotic limit when the number of both eigenvalues goes to infinity and obtained universality results. In this case, the limiting eigenvalue distribution can be supported on 1 or 2 disjoint intervals. We obtained a necessary and sufficient condition on the parameters such that the limiting distribution is supported on 2 disjoint intervals and have computed the eigenvalue density in the limit. Furthermore, by using Riemann-Hilbert analysis, we have shown that under proper rescaling of the eigenvalues, the limiting correlation kernel is given by the sine kernel and the Airy kernel in the bulk and the edge of the spectrum respectively. As a consequence, the behavior of the largest eigenvalue in this model is described by the Tracy-Widom distribution.

• Publication year

  2008

• Venue

  arXiv: Probability

• Publication date

  2008-09-22

• Fields of study

  Mathematics

• Identifiers
  arXiv 0809.3750
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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