The Tracy--Widom limit for the largest eigenvalues of singular complex Wishart matrices

Mathematics – Probability

Scientific paper

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Published in at http://dx.doi.org/10.1214/07-AAP454 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/07-AAP454

This paper extends the work of El Karoui [Ann. Probab. 35 (2007) 663--714] which finds the Tracy--Widom limit for the largest eigenvalue of a nonsingular $p$-dimensional complex Wishart matrix $W_{\mathbb{C}}(\Omega_p,n)$ to the case of several of the largest eigenvalues of the possibly singular $(n

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