A Quick Derivation of the Loop Equations for Random Matrices

Details A Quick Derivation of the Loop Equations for Random Matrices A Quick Derivation of the Loop Equations for Random Matrices

2006-09-18

arxiv.org/abs/math-ph/0609048v1

Physics

Mathematical Physics

Submitted to the MSRI Volume related to the Workshop "Probability, Geometry and Integrable Systems", in celebration of Henry M

Scientific paper

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 equations, originating in the physics of 2-dimensional quantum gravity, have lacked mathematical justification. The goal of this paper is to provide a complete and short proof, relying on a recently established complete asymptotic expansion for the random matrix theory partition function.

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