Costanza Benassi

Northumbria University


Random matrix models, integrable lattices and thermodynamic limit


Mathematical Physics Seminar


4th February 2022, 2:30 pm – 3:30 pm
In your office, Zoom only


Random Matrix models naturally arise in relation to a great variety of problems in mathematics and physics, and constitute a paradigm for the modelling of complex phenomena. We focus on the Hermitian Matrix Ensemble (HME) and Symmetric Matrix Ensemble (SME) and their relationship with integrable hierarchies of nonlinear equations. This relationship is fundamental in the investigation of the features of these models, and in the study of their thermodynamic limit. This talk includes results from C.B, A. Moro (2020) and C.B, M.Dell’Atti, A. Moro (2022). In particular, we show that the HME supports a novel type of phase transition, signalled by a dispersive shock of the relevant order parameter, propagating in the space of coupling constants. On the other hand, in the thermodynamic limit, the order parameters of the SME satisfy a novel integrable hydrodynamic chain of PDEs.





Biography:

Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/31bcbafd10d64d61abf64edae42244091d

Organiser: Thomas Bothner

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