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We consider biorthogonal polynomials that arise in the study of a generalization of two–matrix Hermitian models with two polynomial potentials V 1( x), V 2( y) of any degree, with arbitrary complex coefficients. Finite consecutive subsequences of biorthogonal polynomials (‘‘windows’’), of lengths equal to the degrees of the potentials V 1 and V 2, satisfy systems of ODE’s with polynomial coefficients as well as PDE’s (deformation equations) with respect to the coefficients of the potentials and recursion relations connecting consecutive windows. A compatible sequence of fundamental systems of solutions is constructed for these equations. The (Stokes) sectorial asymptotics of these fundamental systems are derived through saddle-point integration and the Riemann-Hilbert problem characterizing the differential equations is deduced.

Differential Systems for Biorthogonal Polynomials Appearing in 2-Matrix Models and the Associated Riemann?Hilbert Problem