  The first passage time for a single diffusing particle has been studied
extensively, but the first passage time of a system of many diffusing
particles, as is often the case in physical systems, has received little
attention until recently. We consider two models for many particle diffusion --
one treats each particle as independent simple random walkers while the other
treats them as coupled to a common space-time random forcing field that biases
particles nearby in space and time in similar ways. The first passage time of a
single diffusing particle under both of these models show the same statistics
and scaling behavior. However, for many particle diffusions, the first passage
time among all particles (the `extreme first passage time') is very different
between the two models, effected in the latter case by the randomness of the
common forcing field. We develop an asymptotic (in the number of particles and
location where first passage is being probed) theoretical framework to separate
out the impact of the random environment with that of sampling trajectories
within it. We identify a new power-law describing the impact to the extreme
first passage time variance of the environment. Through numerical simulations
we verify that the predictions from this asymptotic theory hold even for
systems with widely varying numbers of particles, all the way down to 100
particles. This shows that measurements of the extreme first passage time for
many-particle diffusions provide an indirect measurement of the underlying
environment in which the diffusion is occurring.
