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Large N expansions and Painlevé hierarchies in the Hermitian matrix model

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Álvarez Galindo, Gabriel and Martínez Alonso, Luis and Medina Reus, Elena (2011) Large N expansions and Painlevé hierarchies in the Hermitian matrix model. Journal of Physics A: Mathematical and Theoretical, 44 (28). ISSN 1751-8113

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Official URL: http://iopscience.iop.org/1751-8121/44/28/285206/pdf/1751-8121_44_28_285206.pdf




Abstract

We present a method to characterize and compute the large N formal asymptotics of regular and critical Hermitian matrix models with general even potentials in the one-cut and two-cut cases. Our analysis is based on a method to solve continuum limits of the discrete string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. This method also leads to an explicit formulation, in terms of coupling constants and critical parameters, of the members of the Painlevé I and Painlevé II hierarchies associated with one-cut and two-cut critical models, respectively.


Item Type:Article
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© 2011 IOP Publishing Ltd. The financial support of the Universidad Complutense under project GR35/10-A910556, the Comision Interministerial de Ciencia y Tecnología under projects FIS2008-00200 and FIS2008-00209 are gratefully acknowledged.

Uncontrolled Keywords:Double Scaling Limit, Partition-Function, Quantum-Gravity, Asymptotics, Universality, Equations, Polynomials, Behavior
Subjects:Sciences > Physics > Physics-Mathematical models
ID Code:20402
Deposited On:05 Apr 2013 10:41
Last Modified:10 Dec 2018 15:09

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