Strongly correlated fermions in a crystal or in an optical lattice in the presence of binary alloy disorder are investigated. We employ the statistical dynamical mean-field theory, which incorporates both, fluctuations due to disorder and local correlations due to interaction, to solve the AndersonHubbard model. Localization due to disorder is studied by means of the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram consisting of disordered correlated metal, Anderson-Mott insulator, and band insulator.

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 correlationinduced 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.

Strongly correlated electrons with box disorder in high-dimensional lattices are investigated. We apply the statistical dynamical mean-field theory, which treats local correlations non-perturbatively. The incorporation of a finite lattice connectivity allows for the detection of disorder-induced localization via the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram and find correlation-induced as well as disorderinduced metal-insulator transitions. Our results qualitatively confirm predictions obtained by typical medium theory. Moreover, we find that the probability distribution function of the local density of states in the metallic phase strongly deviates from a log-normal distribution as found for the non-interacting case.