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arXiv · 1206.3199

Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model

Marco Bertola·Michael Gekhtman·Jacek Szmigielski
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Abstract

We apply the nonlinear steepest descent method to a class of 3x3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two equilibrium measures supported on an arbitrary number of intervals is considered. In this case, we solve the Riemann-Hilbert problem for the outer parametrix in terms of sections of a spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and establish strong asymptotic results for the Cauchy biorthogonal polynomials.

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Marco Bertola, Michael Gekhtman, Jacek Szmigielski. 2012-09-14. Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model. https://doi.org/10.1063/1.4802455

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