The Lenard Recursion Relation and a Family of Singularly Perturbed Matrix Models
Mathematical Physics
2015-10-28 v1 Classical Analysis and ODEs
math.MP
Abstract
We review some aspects of recent work concerning double scaling limits of singularly perturbed hermitian random matrix models and their connection to Painlev\'{e} equations. We present new results showing how a Painlev\'{e} III hierarchy recently proposed by the author can be connected to the Lenard recursion formula used to construct the Painlev\'{e} I and II hierarchies.
Keywords
Cite
@article{arxiv.1502.04954,
title = {The Lenard Recursion Relation and a Family of Singularly Perturbed Matrix Models},
author = {Max R. Atkin},
journal= {arXiv preprint arXiv:1502.04954},
year = {2015}
}
Comments
Based on a talk at "Random Matrix Theory: Foundations and Applications", Cracow, July 1-6 2014, 9 pages