Abstract:Année de publication : 2003
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.
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