Semiclassical expansions in the Toda hierarchy and the hermitian matrix model

Abstract

An iterative algorithm for determining a class of solutions of the dispersionful 2-Toda hierarchy characterized by string equations is developed. This class includes the solution which underlies the large N-limit of the Hermitian matrix model in the one-cut case. It is also shown how the double scaling limit can be naturally formulated in this scheme

22 pages

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Cited by in corpus (3)

• The double scaling limit method in the Toda hierarchy
• An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
• Large N expansions and Painlevé hierarchies in the Hermitian matrix model