DISTRIBUTION OF EIGENVALUES OF CERTAIN MATRIX-ENSEMBLES

We investigate spectral properties of ensembles of NxN random matrices M defined by their probability distribution P(M)=exp[-Tr V(M)] with a weekly confinement potential V(M) for which the moment problem mu(n) = integral x(n)exp[-V(x)]dx is indeterminated. The characteristic prop erty of these ensembles is that the mean density of eigenvalues tends with increasing matrix dimension to be a continuous function contrary to the usual strong confinement cases, where it grows indefinitely whe n N-->infinity. We demonstrate that the standard asymptotic formulas f or correlation functions are not applicable for weakly confinement ens embles and their asymptotic distribution of eigenvalues can deviate fr om the classical ones. The model with V(x)= ln(2)(\x\)/beta is conside red in detail. It is shown that when beta-infinity the unfolded eigenv alue distribution tends to a limit which is different from any standar d random matrix ensembles, but which is the same for all three symmetr y classes: unitary, orthogonal, and symplectic.