  The distribution of times $t_{j,N}$ elapsed until the first $j$ independent
random walkers from a set of $N \gg 1$, all starting from the same site, are
trapped by a quenched configuration of traps randomly placed on a disordered
lattice is investigated. In doing so, the cumulants of the distribution of the
territory explored by $N$ independent random walkers $S_N(t)$ and the
probability $\Phi_N(t)$ that no particle of an initial set of $N$ is trapped by
time $t$ are considered. Simulation results for the two-dimensional incipient
percolation aggregate show that the ratio between the $n$th cumulant and the
$n$th moment of $S_N(t)$ is, for large $N$, (i) very large in comparison with
the same ratio in Euclidean media, and (ii) almost constant. The first property
implies that, in contrast with Euclidean media, approximations of order higher
than the standard zeroth-order Rosenstock approximation are required to provide
a reasonable description of the trapping order statistics. Fortunately, the
second property (which has a geometric origin) can be exploited to build these
higher-order Rosenstock approximations. Simulation results for the
two-dimensional incipient percolation aggregate confirm the predictions of our
approach.
