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Stochastic, deterministic and integrable aspects of random matrix theory

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HY2W04 - Statistical mechanics, integrability and dispersive hydrodynamics

Various important examples of random matrix ensembles have been proven to be intimately connected to Integrable Systems via the properties of their partition functions. The connection lies on the identification of the partition function with the tau function of a particular solution to an integrable hierarchy of nonlinear differential equations. In this talk, we discuss how some stochastic properties of the underlying random matrix ensemble may persist in the thermodynamic limit when order parameters, seen as functions evolving in the space of thermodynamic variables, develop a dispersive shock. A particular, renowned model of Hermitian Random Matrices associated to the Volterra/Kac-van Moerbeke hierarchy will be discussed.

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

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Room S2, Alison Richard Building, 7 West Road, Cambridge, CB3 9DT Senior Parlour, Gonville & Caius College Magdalene College, Magdalene Street

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