TY - JOUR

T1 - Symmetric Matrix Ensemble and Integrable Hydrodynamic Chains

AU - Benassi, Costanza

AU - Dell'Atti, Marta

AU - Moro, Antonio

PY - 2021/5/3

Y1 - 2021/5/3

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

U2 - 10.1007/s11005-021-01416-y

DO - 10.1007/s11005-021-01416-y

M3 - Article

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

M1 - MATH-D-21-00025R1

ER -