Loop models, random matrices and planar algebras
Operator Algebras
2015-05-20 v2 Combinatorics
Abstract
We define matrix models that converge to the generating functions of a wide variety of loop models with fugacity taken in sets with an accumulation point. The latter can also be seen as moments of a non-commutative law on a subfactor planar algebra. We apply this construction to compute the generating functions of the Potts model on a random planar map.
Cite
@article{arxiv.1012.0619,
title = {Loop models, random matrices and planar algebras},
author = {A. Guionnet and V. F. R. Jones and D. Shlyakhtenko and P. Zinn-Justin},
journal= {arXiv preprint arXiv:1012.0619},
year = {2015}
}