On special positive solutions of the first discrete Painlevé hierarchy

Ana filipa Loureiro will carry out joint work with Zélia da Rocha, Semyon Yakubovich, and other members of Analysis Area
Seminar talk:
TITLE: On special positive solutions of the first discrete Painlevé hierarchy
ABSTRACT: The recurrence coefficients of a generalised symmetric Freud weight are positive solutions of a discrete equation in the discrete Painlevé I hierarchy. They also satisfy a coupled system of nonlinear differential equations. Such orthogonality weights also arise in the context of Hermitian matrix models and random symmetric matrix ensembles. In this talk I will report on properties of such special solutions of this integrable system of equations in the dP-I hierarchy, explaining the connections to other areas of mathematics. The emphasis will be on their asymptotic properties.
This is a joint work with Peter Clarkson and Kerstin Jordaan.