TY - JOUR
T1 - Symmetric matrix ensemble and integrable hydrodynamic chains
AU - Dell'Atti, Marta
AU - Moro, Antonio
AU - Benassi, Costanza
PY - 2021/6/14
Y1 - 2021/6/14
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://researchportal.northumbria.ac.uk/en/publications/symmetric-matrix-ensemble-and-integrable-hydrodynamic-chains
U2 - 10.1007/s11005-021-01416-y
DO - 10.1007/s11005-021-01416-y
M3 - Article
SN - 0377-9017
VL - 111
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
M1 - 78
ER -