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The Riemann-Hilbert problems for multiple orthogonal polynomials of types Iand II are used to derive string equations associated to pairs of Lax-Orlovoperators. A method for determining the quasiclassical limit of stringequations in the phase space of the Whitham hierarchy of dispersionlessintegrable systems is provided. Applications to the analysis of the large-nlimit of multiple orthogonal polynomials and their associated random matrixensembles and models of non-intersecting Brownian motions are given.

Multiple orthogonal polynomials, string equations and the large-n limit