Monotonicity and Condensation in Homogeneous Stochastic Particle Systems

Thomas Rafferty, Paul Chleboun, Stefan Grosskinsky

Published 2015-05-08Version 1

We study stochastic particle systems that conserve the particle density and exhibit a condensation transition due to particle interactions. We restrict our analysis to spatially homogeneous systems on finite lattices with stationary product measures, which includes previously studied zero-range or misanthrope processes. All known examples of such condensing processes are non-monotone, i.e. the dynamics do not preserve a partial ordering of the state space and the canonical measures (with a fixed number of particles) are not monotonically ordered. For our main result we prove that homogeneous particle systems with finite critical density are necessarily non-monotone. For infinite critical density condensation can still occur on finite lattices, in this case there also exist monotone condensing processes which we discuss in detail for power law tails.