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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. 398429. ISSN 05503213
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http://arxiv.org/pdf/1101.2727.pdf  Organisation 
http://pdn.sciencedirect.com  Publisher 
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 BleherIts 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 kmaps which does not require the explicit expressions of the coefficients of the topological expansion. Finally we discuss the regularization of singular onecut models within this approach.
Item Type:  Article 

Additional Information:  © 2011 Elsevier B.V. The financial support of the Universidad Complutense under project GR58/08910556 and the Comisión Interministerial de Ciencia y Tecnología under projects FIS200800200 and FIS200800209 are gratefully acknowledged. 
Uncontrolled Keywords:  Graphical Enumeration, PartitionFunction, Asymptotics, Universality, Behavior, Gravity, Polynomials, Limit, Hermitian Matrix Model, Genus Expansion, Counting Maps 
Subjects:  Sciences > Physics > PhysicsMathematical models 
ID Code:  20467 
Deposited On:  21 Mar 2013 11:26 
Last Modified:  10 Dec 2018 15:09 
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