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Título:
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An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
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Autores:
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Álvarez Galindo, Gabriel ;
Martínez Alonso, Luis ;
Medina Reus, Elena
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Tipo de documento:
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texto impreso
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Editorial:
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Elsevier Science BV, 2011-07-11
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Física: Física-Modelos matemáticos
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Tipo = Artículo
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Resumen:
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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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En línea:
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https://eprints.ucm.es/id/eprint/20467/1/alvarez05.pdf
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