Condensation in perturbed zero-range processes

Abstract

Condensation phenomena in zero-range processes have attracted significant attention recently. Here, we consider zero-range processes in which n sites are occupied by m particles that jump between sites according to a jump rate function given by g. Let Z≐(Z1, Z2, …, Zn) denote the steady state of a zero-range process, and let Z*n be the size of the maximum cluster. A non-complete condensation is defined as an event in which Z*n/n converges to a positive constant less than 1 as n tends to infinity. In this work, we provide evidence that condensation depends on the detailed form of the jump rates by showing that non-complete condensation occurs when g is given by where Mk are bounded constants satisfying suitable conditions. Note that this choice of g is a perturbation of which exhibits perfect condensation, i.e. n − Z*n converges to 0 as n tends to infinity.