A Quick Derivation of the Loop Equations for Random Matrices
数学物理
2007-05-23 v1 math.MP
摘要
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.
引用
@article{arxiv.math-ph/0609048,
title = {A Quick Derivation of the Loop Equations for Random Matrices},
author = {N. M. Ercolani and K. D. T-R McLaughlin},
journal= {arXiv preprint arXiv:math-ph/0609048},
year = {2007}
}
备注
Submitted to the MSRI Volume related to the Workshop "Probability, Geometry and Integrable Systems", in celebration of Henry McKean's 75th birthday