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.| File | Dimensione | Formato | |
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Bertola-Gekhtman-Szmigielski-Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model.pdf
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