  We investigate first-passage statistics of an ensemble of N noninteracting
random walks on a line. Starting from a configuration in which all particles
are located in the positive half-line, we study S_n(t), the probability that
the nth rightmost particle remains in the positive half-line up to time t. This
quantity decays algebraically, S_n (t) ~ t^{-beta_n}, in the long-time limit.
Interestingly, there is a family of nontrivial first-passage exponents,
beta_1<beta_2<...<beta_{N-1}; the only exception is the two-particle case where
beta_1=1/3. In the N-->infinity limit, however, the exponents attain a scaling
form, beta_n(N)--> beta(z) with z=(n-N/2)/sqrt{N}. We also demonstrate that the
smallest exponent decays exponentially with N. We deduce these results from
first-passage kinetics of a random walk in an N-dimensional cone and confirm
them using numerical simulations. Additionally, we investigate the family of
exponents that characterizes leadership statistics of multiple random walks and
find that in this case, the cone provides an excellent approximation.
