  We consider the dynamics of the disordered, one-dimensional, symmetric zero
range process in which a particle from an occupied site $k$ hops to its nearest
neighbour with a quenched rate $w(k)$. These rates are chosen randomly from the
probability distribution $f(w) \sim (w-c)^{n}$, where $c$ is the lower cutoff.
For $n > 0$, this model is known to exhibit a phase transition in the steady
state from a low density phase with a finite number of particles at each site
to a high density aggregate phase in which the site with the lowest hopping
rate supports an infinite number of particles. In the latter case, it is
interesting to ask how the system locates the site with globally minimum rate.
We use an argument based on local equilibrium, supported by Monte Carlo
simulations, to describe the approach to the steady state. We find that at
large enough time, the mass transport in the regions with a smooth density
profile is described by a diffusion equation with site-dependent rates, while
the isolated points where the mass distribution is singular act as the
boundaries of these regions. Our argument implies that the relaxation time
scales with the system size $L$ as $L^{z}$ with $z=2+1/(n+1)$ for $n > 1$ and
suggests a different behaviour for $n < 1$.
