  In this paper we present results of the lowest eigenvalues of random
Hamiltonians for both fermion and boson systems. We show that an empirical
formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of
energy centroids and widths of eigenvalues are applicable to many different
systems (except for $d$ boson systems). We improve the accuracy of the formula
by adding moments higher than two. We suggest another new formula to evaluate
the lowest eigenvalues for random matrices with large dimensions (20-5000).
These empirical formulas are shown to be applicable not only to the evaluation
of the lowest energy but also to the evaluation of excited energies of systems
under random two-body interactions.
