  Statistical properties of the front of a semi-infinite system of single-file
diffusion (one dimensional system where particles cannot pass each other, but
in-between collisions each one independently follow diffusive motion) are
investigated. Exact as well as asymptotic results are provided for the
probability density function of (a) the front-position, (b) the maximum of the
front-positions, and (c) the first-passage time to a given position. The
asymptotic laws for the front-position and the maximum front-position are found
to be governed by the Fisher-Tippett-Gumbel extreme value statistics. The
asymptotic properties of the first-passage time is dominated by a
stretched-exponential tail in the distribution. The farness of the front with
the rest of the system is investigated by considering (i) the gap from the
front to the closest particle, and (ii) the density profile with respect to the
front-position, and analytical results are provided for late time behaviors.
