English

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