2021/01/31 by Costanza Benassi, Marta Dell'Atti, Antonio Moro · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1007/s11005-021-01416-y
22 pages. Some typos have been corrected. The introduction has been revised. Appendix A has been added
arxiv created 2021/04/13 · arxiv updated 2021/06/30
The partition function of the Symmetric Matrix Ensemble is identified with the τ-function of a particular solution of the Pfaff Lattice. We show that in the case of even power interactions, in the thermodynamic limit, the τ-function corresponds to the solution of an integrable chain of hydrodynamic type. We prove that the hydrodynamic chain so obtained is diagonalisable and admits hydrodynamic reductions in Riemann invariants in an arbitrary number of components.