Symmetric Matrix Ensemble and Integrable Hydrodynamic Chains
Mathematical Physics
2021-06-30 v2 math.MP
Exactly Solvable and Integrable Systems
Abstract
The partition function of the Symmetric Matrix Ensemble is identified with the function of a particular solution of the Pfaff Lattice. We show that in the case of even power interactions, in the thermodynamic limit, the 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.
Keywords
Cite
@article{arxiv.2101.10232,
title = {Symmetric Matrix Ensemble and Integrable Hydrodynamic Chains},
author = {Costanza Benassi and Marta Dell'Atti and Antonio Moro},
journal= {arXiv preprint arXiv:2101.10232},
year = {2021}
}
Comments
22 pages. Some typos have been corrected. The introduction has been revised. Appendix A has been added