On special function positive solutions of the first discrete Painlevé hierarchy 

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• Ana Loureiro (University of Kent)
• Friday 04 November 2022, 11:20-12:10
• Seminar Room 1, Newton Institute.

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AR2W02 - Mathematics of beyond all-orders phenomena

The recurrence coefficients in the three-term recurrence relation of a polynomial sequence orthogonal with respect to a quartic or a sextic Freud weights satisfy a forth order discrete equation which is a member of the first discrete Painlevé hierarchy. They also satisfy a coupled system of second-order, 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 recurrence coefficients and explain how the study may inform on the study of recurrence coefficients associated with higher order Freud weights. The emphasis will be on their asymptotic properties.    Collaborators: Peter Clarkson (University of Kent) and Kerstin Jordaan (University of South Africa)

This talk is part of the Isaac Newton Institute Seminar Series series.

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