  We investigate the first passage time t_{j,N} to a given chemical or
Euclidean distance of the first j of a set of N>>1 independent random walkers
all initially placed on a site of a disordered medium. To solve this
order-statistics problem we assume that, for short times, the survival
probability (the probability that a single random walker is not absorbed by a
hyperspherical surface during some time interval) decays for disordered media
in the same way as for Euclidean and some class of deterministic fractal
lattices. This conjecture is checked by simulation on the incipient percolation
aggregate embedded in two dimensions. Arbitrary moments of t_{j,N} are
expressed in terms of an asymptotic series in powers of 1/ln N which is
formally identical to those found for Euclidean and (some class of)
deterministic fractal lattices. The agreement of the asymptotic expressions
with simulation results for the two-dimensional percolation aggregate is good
when the boundary is defined in terms of the chemical distance. The agreement
worsens slightly when the Euclidean distance is used.
