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SUMMARY:Random matrix models\, integrable lattices and thermodynamic limit
  - Costanza Benassi (Northumbria University)
DTSTART:20220718T093000Z
DTEND:20220718T100000Z
UID:TALK176075@talks.cam.ac.uk
DESCRIPTION:Random Matrix models naturally arise in relation to a great va
 riety of problems in mathematics and physics\, and constitute a paradigm f
 or the modelling of complex phenomena. We focus on the Hermitian Matrix En
 semble (HME) and Symmetric Matrix Ensemble (SME) and their relationship wi
 th integrable hierarchies of nonlinear equations. This relationship is fun
 damental 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&rsquo\;Atti\, A. Moro (2021). In particul
 ar\, we show that the HME supports a novel type of phase transition\, sign
 alled by a dispersive shock of the relevant order parameter\, propagating 
 in the space of coupling constants. On the other hand\, in the thermodynam
 ic limit\, the order parameters of the SME satisfy a novel integrable hydr
 odynamic chain of PDEs.
LOCATION:Seminar Room 1\, Newton Institute
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