Exact Solution for a class of Mass Transport Models, Condensation Transitions, and the Nature of the Condensate

We study the phenomenon of real space condensation in the steady state of one dimensional mass transport models. These models, including the Zero-Range Process and the Asymmetric Random Average Process, have been used to describe a variety of physical systems, e.g., bio-molecular motors, vehicular or pedestrian traffic, force propagation through granular media, etc. The dynamics consists of stochastically transferring a portion of the mass, from site to neighboring site, according to some prescribed distribution. For a class of these models, we find an easy test to check if the steady state (full multi-site) distribution is `factorizable,' and if so, a simple method to construct the solution explicitly. Based on this approach, we not only verify the criterion for the existence of a condensation transition (where, a la Bose-Einstein, a finite fraction of the total mass condenses into a single site) but also elucidate the nature of the condensate. Specifically, we find two regimes: one where the mass of the condensate is Gaussian distributed with normal fluctuations, and a second regime with non-Gaussian distributions and anomalously large fluctuations.