Álvarez Galindo, GabrielMartínez Alonso, LuisMedina Reus, Elena2023-06-202023-06-202011-07-110550-321310.1016/j.nuclphysb.2011.02.019https://hdl.handle.net/20.500.14352/43708© 2011 Elsevier B.V. The financial support of the Universidad Complutense under project GR58/08-910556 and the Comisión Interministerial de Ciencia y Tecnología under projects FIS2008-00200 and FIS2008-00209 are gratefully acknowledged.We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the Bleher-Its deformation of the model, on its associated integral representation of the free energy, and on a method for solving the string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. As a byproduct we obtain an efficient algorithm to compute generating functions for the enumeration of labeled k-maps which does not require the explicit expressions of the coefficients of the topological expansion. Finally we discuss the regularization of singular one-cut models within this approach.engjournal articlehttp://pdn.sciencedirect.com/science?_ob=MiamiImageURL&_cid=271560&_user=144492&_pii=S0550321311001246&_check=y&_origin=article&_zone=toolbar&_coverDate=11-Jul-2011&view=c&originContentFamily=serial&wchp=dGLbVlV-zSkWz&md5=e155f623a2d9c04bb489d6b9a45028c8&http://arxiv.org/pdf/1101.2727.pdfhttp://pdn.sciencedirect.comopen access51-73Graphical EnumerationPartition-FunctionAsymptoticsUniversalityBehaviorGravityPolynomialsLimitHermitian Matrix ModelGenus ExpansionCounting MapsFísica-Modelos matemáticos