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math-ph2006★ 2 cited
A Quick Derivation of the Loop Equations for Random Matrices
N. M. Ercolani, K. D. T-R McLaughlin
The "loop equations" of random matrix theory are a hierarchy of equations born of attempts to obtain explicit formulae for generating functions of map enumeration problems. These e…
math-ph2006
Random Matrices, Graphical Enumeration and the Continuum Limit of Toda Lattices
N. M. Ercolani, K. D. T-R McLaughlin, V. U. Pierce
In this paper we derive a hierarchy of differential equations which uniquely determine the coefficients in the asymptotic expansion, for large , of the logarithm of the partitio…