  In this paper we investigate the effect of repulsive pair interactions on
Bose-Einstein condensation in a well-established random one-dimensional system
known as the Luttinger-Sy model at positive temperature. We study separately
hard core interactions as well as a class of more general repulsive
interactions, also allowing for a scaling of certain interaction parameters in
the thermodynamic limit. As a main result, we prove in both cases that for
sufficiently strong interactions all eigenstates of the non-interacting
one-particle Luttinger-Sy Hamiltonian as well as any sufficiently localized
one-particle state are almost surely not macroscopically occupied.
