An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
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 re...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/43708 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/43708 |
| Access Level: | acceso abierto |
| Palabra clave: | 51-73 Graphical Enumeration Partition-Function Asymptotics Universality Behavior Gravity Polynomials Limit Hermitian Matrix Model Genus Expansion Counting Maps Física-Modelos matemáticos |
| Sumario: | 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. |
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