TY - JOUR
T1 - Symmetric Matrix Ensemble and Integrable Hydrodynamic Chains
AU - Benassi, Costanza
AU - Dell'Atti, Marta
AU - Moro, Antonio
N1 - Funding information: This work is supported by the Leverhulme Trust RPG 2017-228 (PI A.M.). Authors also thank the London Mathematical Society, the Royal Society International Exchanges Grant IES-R2-170116 (PI A.M.), GNFM - Gruppo Nazionale per la Fisica Matematica, INdAM (Istituto Nazionale di Alta Matematica) for supporting activities that contributed to the research reported in this paper.
PY - 2021/6
Y1 - 2021/6
N2 - 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.
AB - 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.
KW - Random Matrices
KW - Hydrodynamic Integrable Systems
KW - Hydrodynamic Reductions
KW - Gibbons-Tsarev Systems
UR - https://www.scopus.com/pages/publications/85107911183
U2 - 10.1007/s11005-021-01416-y
DO - 10.1007/s11005-021-01416-y
M3 - Article
SN - 0377-9017
VL - 1113
SP - 1
EP - 25
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
M1 - 78
ER -