Publication: Large N expansions and Painlevé hierarchies in the Hermitian matrix model
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2011-07-15
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IOP Publishing Ltd
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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.
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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.
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