  What is the connection of random matrices with integrable systems? Is this
connection really useful? Introducing apprpriate times in the distribution of
the ensemble of matrices, one shows that the corresponding distribution of the
eigenvalues satisfies the KP-equation, the 1-Toda lattice or the 2-Toda
lattice, depending on the original distribution. The probability distribution
also satisfies Virasoro type constraints, which contain a time-part and a
boundary-part. These equations taken together lead to a system of PDE's for the
distribution of the spectrum in terms of the boundary of the set, under
consideration.
