Zero range processes with decreasing jump rates can equilibrate in a condensed phase when the particle density exceeds a critical value. In this phase a nontrivial fraction of the mass in the system concentrates on a single randomly located site, the condensate. At a suitably long time scale the location of the condensate changes. We consider a supercritical nearest neighbour symmetric zero range process on the discrete 1d torus. We show that the scaling limit of the condensate dynamics is a Lévy process on the unit torus with jump rates inversely proportional to the jump length.
Joint work with Inés Armendáriz and Stefan Grosskinsky