  We consider the spherical Sherrington-Kirkpatrick model of spin glass with
sparse interaction, where the interactions between most of the pairs of the
spin variables are possibly zero. With suitable normalization, we prove that
the limiting free energy does not depend on the sparsity whereas the
fluctuation of the free energy does. We also prove that both in the high- and
the low-temperature regimes the fluctuation of the free energy converges in
distribution to Gaussian distributions of same order when the sparsity is on a
certain level, but their variances are different.
