The Lenard Recursion Relation and a Family of Singularly Perturbed Matrix Models
M. Atkin · Acta Physica Polonica B · 2015
We review some aspects of recent work concerning double scaling limits of singularly perturbed hermitian random matrix models and their connection to Painlevé equations. We present new results showing how a Painlevé III hierarchy recently proposed by the author can be connected to the Lenard recursion formula used to construct the Painlevé I and II hierarchies.