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We study the eigenvalue behaviour of large complex correlated Wishart matrices near an interior point of the limiting spectrum where the density vanishes (cusp point), and refine the existing results at the hard edge as well.
1928
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I.M. Johnstone, On the distribution of the largest eigenvalue in principal components analysis , Ann. Statist., 29
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J. Baik, G. Ben Arous, S. Péché, Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices , Ann. Probab. 33
2005
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B. Simon, Trace ideals and their applications , Mathematical Surveys and Monographs 120, second edition, American Mathematical Society, Providence, RI, 2005
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J. B. Hough, M. Krishnapur, Y. Peres, B. Virág, Determinantal processes and independence , Probab. Surveys 3
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K. Johansson, Random matrices and determinantal processes , Mathematical Statistical Physics: Lecture Notes of the Les Houches Summer School 2005 (Bovier et al., eds.), Elsevier, 2006, 1–55
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M. Y. Mo, Universality in complex Wishart ensembles for general covariance matrices with 2 distinct eigenvalues , Journal of Multivariate Analysis 101
2009
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M. Adler, M. Cafasso, P. van Moerbeke, Nonlinear PDEs for gap probabilities in random matrices and KP theory , Physica D: Nonlinear Phenomena 241
2012
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M. Bertola, M. Cafasso, The transition between the gap probabilities from the Pearcey to the Airy Process; a Riemann–Hilbert approach , Int. Math. Res. Not. 2012 no. 7, 1519–1568
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2014
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C. Tracy, H. Widom, The Pearcey process , Commun. Math. Phys. 263
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P. M. Bleher, A.B.J. Kuijlaars, Large n limit of Gaussian random matrices with external source, part III: double scaling limit , Comm. Math. Phys. 270
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N. El Karoui, Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices , Ann. Probab. 35
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A. Okounkov, N. Reshetikhin, Random skew plane partitions and the Pearcey process , Comm. Math. Phys. 269
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A. Onatski, The Tracy-Widom limit for the largest eigenvalues of singular complex Wishart matrices , Ann. Appl. Probab. 18
2008
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G. Anderson, A. Guionnet, O. Zeitouni, An Introduction to Random Matrices , Cambridge University Press, 2009
2009
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E. Duse, A. Metcalfe, Universal edge fluctuations of discrete interlaced particle systems . In preparation
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2014
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2014
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2014
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2014
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