A note on biorthogonal ensembles

• Autores: Patrick Desrosiers, Peter J. Forrester
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 152, Nº 2, 2008, págs. 167-187
• Idioma: inglés
• DOI: 10.1016/j.jat.2007.08.006
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• Resumen

  • 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.