  We study the phase diagram of the zero-temperature, one-dimensional
Bose-Fermi-Hubbard model for fixed fermion density in the limit of small
fermionic hopping. This model can be regarded as an instance of a disordered
Bose-Hubbard model with dichotomic values of the stochastic variables. Phase
boundaries between compressible, incompressible (Mott-insulating) and partially
compressible phases are derived analytically within a generalized
strong-coupling expansion and numerically using density matrix renormalization
group (DMRG) methods. We show that first-order correlations in the partially
compressible phases decay exponentially, indicating a glass-type behaviour.
Fluctuations within the respective incompressible phases are determined using
perturbation theory and are compared to DMRG results.
