Ground state spin 0^+ dominance of many-body systems with random interactions and related topics

In this talk we shall show our recent results in understanding the spin$^{\rm parity}$ 0$^+$ ground state (0 g.s.) dominance of many-body systems. We propose a simple approach to predict the spin $I$ g.s. probabilities which does not require the diagonalization of a Hamiltonian with random interactions. Some findings related to the 0 g.s. dominance will also be discussed.