Symmetric matrix ensemble and integrable hydrodynamic chains

Marta Dell'Atti, Antonio Moro, Costanza Benassi

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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.
Original languageEnglish
Article number78
Number of pages25
JournalLetters in Mathematical Physics
Publication statusPublished - 14 Jun 2021


  • Random matrices
  • Hydrodynamic integrable systems
  • · Hydrodynamic reductions
  • Gibbons–Tsarev systems


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