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Orthogonal Polynomials and Symmetric Sextic Freud weights

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HY2W04 - Statistical mechanics, integrability and dispersive hydrodynamics

In this talk I will discuss orthogonal polynomials associated with symmetric sextic Freud weights. In particular I will describe properties of the recurrence coefficients in the three-term recurrence relation associated with these orthogonal polynomials. These recurrence coefficients satisfy a fourth-order discrete equation which is the second member of the first discrete Painleve hierarchy, also known as the string equation, and also satisfies a coupled system of second-order, nonlinear differential equations. The weight arises in the context of Hermitian matrix models and random symmetric matrix ensembles.   Collaborators: Kerstin Jordaan (University of South Africa), Ana Loureiro (University of Kent).

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

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