Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight (Q2419266)

This paper is a continuation of a paper by the authors [Adv. Math. 302, 1137--1232 (2016; Zbl 1354.31002)]. They study the zero distribution of multiple orthogonal polynomials (MOPs) with complex zeros that exhibit non-hermitian orthogonality on unbounded sets with no possibility of reduction to real orthogonality. Besides the quadratic differentials their main asymptotic tool is the matrix Riemann-Hilbert problem characterization of MOPs with cubic weights and the development of the Deift-Zhon nonlinear steepest descent method, that yields not only the limiting zero distribution but a detailed uniform asymptotics of the polynomial on the whole complex plane.