Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model
Exactly Solvable and Integrable Systems
2015-06-05 v2
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.
Cite
@article{arxiv.1206.3199,
title = {Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model},
author = {Marco Bertola and Michael Gekhtman and Jacek Szmigielski},
journal= {arXiv preprint arXiv:1206.3199},
year = {2015}
}
Comments
31 pages, 12 figures. V2; typos corrected, added references