The Lenard Recursion Relation and a Family of Singularly Perturbed Matrix Models
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.
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