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.

Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model / Bertola, M.; Gekhtman, M.; Szmigielski, J.. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 54:4(2013), pp. 1-25. [10.1063/1.4802455]

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

Bertola, M.;
2013-01-01

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.
2013
54
4
1
25
043517
https://arxiv.org/abs/1206.3199
https://aip.scitation.org/doi/10.1063/1.4802455
Bertola, M.; Gekhtman, M.; Szmigielski, J.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12210
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