  We establish a conceptual relation between the fluctuations of the local
density of states (LDOS) and intensity correlations in speckle patterns
resulting from multiple scattering of waves in random media. We show that among
known types of speckle correlations (C1, C2, C3, and C0) only C0 contributes to
LDOS fluctuations in the infinite medium. We propose to exploit the equivalence
of LDOS fluctuations and C0 intensity correlation as a `selection rule' for
scattering processes contributing to C0.
