A note on biorthogonal ensembles |
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Authors: | Patrick Desrosiers Peter J Forrester |
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Institution: | aDepartment of Mathematics and Statistics, University of Melbourne, Parkville, Vic. 3010, Australia |
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Abstract: | We study multiple orthogonal polynomials in the context of biorthogonal ensembles of random matrices. In these ensembles, the eigenvalue probability density function factorizes into a product of two determinants while the eigenvalue correlation functions can be written as a determinant of a kernel function. We show that the kernel is itself an average of a single ratio of characteristic polynomials. In the same vein, we prove that the type I multiple polynomials can be expressed as an average of the inverse of a characteristic polynomial. We finally introduce a new biorthogonal matrix ensemble, namely the chiral unitary perturbed by a source term, whose multiple polynomials are related to the modified Bessel function of the first kind. |
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Keywords: | Multiple polynomials Random matrices |
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