Order parameters for unitary ensembles solve the modified KP equation via the Volterra lattice while orthogonal ensembles yield a new integrable chain via the Pfaff lattice, with thermodynamic limits being hydrodynamic-type systems solved by the same semi-discrete dynamical chain.
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Random matrix ensembles and integrable differential identities
Order parameters for unitary ensembles solve the modified KP equation via the Volterra lattice while orthogonal ensembles yield a new integrable chain via the Pfaff lattice, with thermodynamic limits being hydrodynamic-type systems solved by the same semi-discrete dynamical chain.