Universal Large Deviations for the Tagged Particle in Single File Motion

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.