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We study the averaged product of characteristic polynomials of large random matrices in the Gaussian beta-ensemble perturbed by an external source of finite rank.
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2005
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P. Desrosiers and P. J. Forrester, Asymptotic correlations for Gaussian and Wishart matrices with external source
2006
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P. Desrosiers and P. J. Forrester, Hermite and Laguerre β \beta -ensembles: Asymptotic corrections to the eigenvalue density
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S. Péché, The largest eigenvalue of small rank perturbations of Hermitian random matrices
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J. Baik and D. Wang, On the Largest Eigenvalue of a Hermitian Random Matrix Model with Spiked External Source I. Rank 1 Case
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M. Bertola, R. Buckingham, S. Y. Lee, V. Pierce, Spectra of Random Hermitian Matrices with a Small-Rank External Source: The Critical and Near-Critical Regimes
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2008
Cited alongside, same era.
P. Desrosiers and P. J. Forrester, A note on biorthogonal ensembles
2008
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M. Adler, J. Delépine and P. van Moerbeke, Dyson’s nonintersecting Brownian motions with a few outliers
2009
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K. E. Bassler, P. J. Forrester and N. E. Frankel, Eigenvalue separation in some random matrix models , J. Math. Phys. 5
2009
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P. Desrosiers, Duality in random matrix ensembles for all β \beta
2009
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B. Valkó and B. Virág, Continuum limits of random matrices and the Brownian carousel
2009
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S. Delvaux, Average characteristic polynomials for multiple orthogonal polynomial ensembles
2010
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2012
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P. Bourgade, L. Erdös, and H. Yau, Bulk universality of general β \beta -ensembles with non-convex potential
2012
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M. Y. Mo, Rank 1 real Wishart spiked model
2012
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D. Wang, The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, part I
2012
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A. Bloemendal and B. Virág, Limits of spiked random matrices I
2013
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2013
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P. J. Forrester, The averaged characteristic polynomial for the Gaussian and chiral Gaussian ensembles with a source
2013
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