Abundance of ground states with positive parity

We investigate analytically and numerically a random-matrix model for m fermions occupying center dot(1) single-particle states with positive parity and center dot(2) single-particle states with negative parity and interacting through random two-body forces that conserve parity. The single-particle states are completely degenerate and carry no further quantum numbers. We compare spectra of many-body states with positive and with negative parity. We show that in the dilute limit defined by m,center dot(1,2)->infinity and m/center dot(1,2)-> 0, ground states with positive and negative parity occur with equal probability. Differences in the ground-state probabilities are, thus, a finite-size effect and are mainly due to different dimensions of the Hilbert spaces of either parity.