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Álvarez Galindo, Gabriel and Martínez Alonso, Luis and Medina Reus, Elena
(2011)
*An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model.*
Nuclear Physics B, 848
(2).
pp. 398-429.
ISSN 0550-3213

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## Abstract

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.

Item Type: | Article |
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Additional Information: | © 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. |

Uncontrolled Keywords: | Graphical Enumeration, Partition-Function, Asymptotics, Universality, Behavior, Gravity, Polynomials, Limit, Hermitian Matrix Model, Genus Expansion, Counting Maps |

Subjects: | Sciences > Physics > Physics-Mathematical models |

ID Code: | 20467 |

Deposited On: | 21 Mar 2013 11:26 |

Last Modified: | 31 Dec 2020 00:01 |

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