  One-dimensional free fermions are studied with emphasis on propagating fronts
emerging from a step initial condition. The probability distribution of the
number of particles at the edge of the front is determined exactly. It is found
that the full counting statistics coincides with the eigenvalue statistics of
the edge spectrum of matrices from the Gaussian unitary ensemble. The
correspondence established between the random matrix eigenvalues and the
particle positions yields the order statistics of the right-most particles in
the front and, furthermore, it implies their subdiffusive spreading.
