Chain of matrices, loop equations and topological recursion
Mathematical Physics
2009-11-30 v1 High Energy Physics - Theory
math.MP
Abstract
Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. These two definitions, perturbative and non-perturbative, are discussed in this chapter as well as their relation. The so-called loop equations satisfied by integrals over random matrices coupled in chain is discussed as well as their recursive solution in the perturbative case when the matrices are Hermitean.
Cite
@article{arxiv.0911.5089,
title = {Chain of matrices, loop equations and topological recursion},
author = {Nicolas Orantin},
journal= {arXiv preprint arXiv:0911.5089},
year = {2009}
}
Comments
28 pages, 1 figure, contribution to The Oxford Handbook of Random Matrix Theory