  Strongly correlated fermions in three- and two-dimensional optical lattices
with experimentally realistic speckle disorder are investigated. We extend and
apply the statistical dynamical mean-field theory, which treats local
correlations non-perturbatively, to incorporate on-site and hopping-type
randomness on equal footing. Localization due to disorder is detected via the
probability distribution function of the local density of states. We obtain a
complete paramagnetic ground state phase diagram for experimentally realistic
parameters and find a strong suppression of the correlation-induced metal
insulator transition due to disorder. Our results indicate that the
Anderson-Mott and the Mott insulator are not continuously connected due to the
specific character of speckle disorder. Furthermore, we discuss the effect of
finite temperature on the single-particle spectral function.
