  We consider a gas of point particles moving in a one-dimensional channel with
a hard-core inter-particle interaction that prevents particle crossings ---
this is called single-file motion. Starting from equilibrium initial conditions
we observe the motion of a tagged particle. It is well known that if the
individual particle dynamics is diffusive, then the tagged particle motion is
sub-diffusive, while for ballistic particle dynamics, the tagged particle
motion is diffusive. Here we compute exactly the large deviation function for
the tagged particle displacement and show that this is universal, independent
of the individual dynamics.
