  We study interacting Bose gases of dimensions $2\le d \in \mathbb N$ at zero
temperature in a random model known as the Kac-Luttinger model. Choosing the
pair-interaction between the bosons to be of a mean-field type, we prove
(complete) Bose-Einstein condensation in probability or with probability almost
one into the minimizer of a Hartree-type functional. We accomplish this by
building upon very recent results by Alain-Sol Sznitman on the spectral gap of
the noninteracting Bose gas.
