It is well-known that the partition function of the unitary ensembles of random matrices is given by a τ -function of the Toda lattice hierarchy and those of the orthogonal and symplectic ensembles are τ -functions of the Pfaff lattice hierarchy. In these cases the asymptotic expansions of the free energies given by the logarithm of the partition functions lead to the dispersionless (i.e. conti...
