Скачать или смотреть A short course on Integrability and Complexity: Lecture 4

This short course aims at illustrating the connection between statistical mechanical models and nonlinear integrable partial differential equations (PDEs) through concrete examples. The mean field Potts model is chosen as a prototype of classical spin systems and we demonstrate its solvability in terms of integrable viscous PDEs. Unitary and orthogonal random matrix ensembles are considered as prototypes of complex systems and, following the work of Adler, van Moerbeke and collaborators, we illustrate their connection to integrable lattice models and, based on recent developments by Benassi-Dell'Atti-Moro, to integrable systems of PDEs of hydrodynamic type.

Lecture 4 : Integrable differential identities for the orthogonal ensemble