$\frak{H}$ in this case is also much more complicated and a thorough analysis of this set making use of properties of harmonic functions is carried out in Section \[se:geo\].

For theoretical reasons, the model studied in this paper is crucial in understanding of the phase transition behavior that occurs in Wishart ensembles. (See [@Baik95]). When the 2 intervals in the support of $F$ closes up, a phase transition takes place and the correlation kernel will demonstrate a different behavior at the point where the support closes up. With the Riemann-Hilbert technique used in this paper, such behavior can be studied rigorously as in [@BKdou] and the eigenvalue correlation function near the critical point will be given by the Pearcey kernel. For practical reasons, many covariance matrices appearing in fields of science are not finite perturbations of the identity matrix. In fact, covariance matrices that have groups of distinct eigenvalues are accepted models in various areas such as the correlation of genes in microarray analysis and the correlation of the returns of stocks in finance.

Acknowledgement {#acknowledgement .unnumbered}
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The author acknowledges A. Kuijlaars for pointing out reference [@Lysov] to me and EPSRC for the financial support provided by the grant 