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

On Bose-Einstein condensation in interacting Bose gases in the Kac-Luttinger model