  Diffusion in a one dimensional random force field leads to interesting
localisation effects, which we study using the equivalence with a directed walk
model with traps. We show that although the average dispersion of positions
$\bar{< x^2 > - < x > ^2}$ diverges for long times, the probability that two
particles occupy the same site tends to a finite constant in the small bias
phase of the model. Interestingly, the long time properties of this
off-equilibrium, aging phase is similar to the equilibrium phase of the Random
Energy Model.
