Martínez Alonso, LuisMedina Reus, Elena2023-06-202023-06-202009-03-221751-811310.1088/1751-8113/42/20/205204https://hdl.handle.net/20.500.14352/44794©IOP Publishing Ltd. The authors wish to thank the Spanish Ministerio de Educación y Ciencia (research project FIS2008-00200/FIS) for its finantial support. This work is also part of the MISGAM programme of the European Science Foundation.The Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated with pairs of Lax-Orlov operators. A method for determining the quasiclassical limit of string equations in the phase space of the Whitham hierarchy of dispersionless integrable systems is provided. Applications to the analysis of the large-n limit of multiple orthogonal polynomials and their associated random matrix ensembles and models of non-intersecting Brownian motions are given.engjournal articlehttp://dx.doi.org/10.1088/1751-8113/42/20/205204http://iopscience.iop.org/http://arxiv.org/abs/0812.3817open access51-73Gaussian random matricesNonintersecting brownian motionsUniversal whitham hierarchyExternal sourceModelsFísica-Modelos matemáticosFísica matemática