Statics and dynamics of a zero-range process with saturated condensation

I will present an overview of a class of one dimensional zero-range processes in which the real-space condensation phenomenon does not occur and is replaced by a saturated condensation: that is, an extensive number of finite-size condensates in the steady state. We determined the conditions under which this occurs, and investigated the dynamics of relaxation to the steady state. Those dynamics can be naturally identified with two distinct stages: a rapid initial growth of condensates followed by a slow process of activated evaporation and condensation. I will sketch the calculation of the early time dynamics under a mean-field approximation, the equilibrium evaporation and condensation rates with a first-passage time calculation and the non-equilibrium relaxation using a fluctuation-dissipation type approach.