  We consider systems of particles hopping stochastically on $d$-dimensional
lattices with space-dependent probabilities. We map the master equation onto an
evolution equation in a Fock space where the dynamics are given by a quantum
Hamiltonian (continuous time) or a transfer matrix resp. (discrete time). We
show that under certain conditions the time-dependent two-point density
correlation function in the $N$-particle steady state can be computed from the
probability distribution of a single particle moving in the same environment.
Focussing on exclusion models where each lattice site can be occupied by at
most one particle we discuss as an example for such a stochastic process a
generalized Heisenberg antiferromagnet where the strength of the spin-spin
coupling is space-dependent. In discrete time one obtains for one-dimensional
systems the diagonal-to-diagonal transfer matrix of the two-dimensional
six-vertex model with space-dependent vertex weights. For a random distribution
of the vertex weights one obtains a version of the random barrier model
describing diffusion of particles in disordered media. We derive exact
expressions for the averaged two-point density correlation functions in the
presence of weak, correlated disorder.
