Monotonicity and condensation in homogeneous stochastic particle systems

Journal article

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 condensing homogeneous particle systems with finite critical density are necessarily non-monotone. On finite lattices condensation can occur even when the critical density is infinite, in this case we give an example of a condensing process that numerical evidence suggests is monotone, and give a partial proof of its monotonicity.

Authors: Rafferty, T; Chleboun, P; Grosskinsky, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Institute of Mathematical Statistics
• Journal: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
• Volume: 54
• Issue: 2
• Pages: 790-818
• Publication date: 2018-04-25
• Acceptance date: 2017-02-06
• DOI: 10.1214/17-AIHP821
• ISSN: 1424-0661
• Keywords: cond-mat.stat-mech; math.PR