A Riemann-Hilbert problem for biorthogonal polynomials

TL;DR

This paper formulates a new Riemann-Hilbert problem to characterize biorthogonal polynomials in coupled random matrices, offering a potentially more tractable approach for asymptotic analysis compared to previous methods.

Contribution

It introduces a novel Riemann-Hilbert problem for biorthogonal polynomials that differs from existing formulations, facilitating future asymptotic studies.

Findings

New Riemann-Hilbert formulation for biorthogonal polynomials

Potential for asymptotic analysis of coupled random matrices

Comparison with existing Riemann-Hilbert problems

Abstract

We characterize the biorthogonal polynomials that appear in the theory of coupled random matrices via a Riemann-Hilbert problem. Our Riemann-Hilbert problem is different from the ones that were proposed recently by Ercolani and McLaughlin, Kapaev, and Bertola et al. We believe that our formulation may be tractable to asymptotic analysis.