  We analyze several ground state related properties of mesoscopic systems
using the random interaction matrix model EGOE(1+2)-$\cs$ (or RIMM) for many
fermion systems with spin degree of freedom and the Hamiltonian containing
pairing and exchange interactions in addition to the mean-field one-body and
random two-body parts. RIMM reproduces the essential features of various
properties: odd-even staggering in ground state energies as a function of
particle number, delay in ground state magnetization and conductance peak
spacing distributions. The analytical formula, we have derived, for the
ensemble averaged spectral variances provides a simple understanding of some of
these properties.
