Driven diffusive systems and growing stationary configurations

We study attractive particle systems with stationary product measures. We utilize the property of attractivity and its link to coupling to build a growth process that samples from the stationary measure of the zero-range process, on fixed and finite lattices, with computation times scaling linearly with the number of particles N . The zero-range process with constant jump-rates and a single defect site is known to exhibit a condensation transition, and we use L independent continuous time birth-processes to sample from the stationary measure that exhibits condensation. The birth-rate of the defect site is a time inhomogeneous process, where the intensity function (or time integrated birth-rate) exhibits the property of finite-time-blow-up. For this process, finite-time-blow-up implies that infinitely many events can occur in a finite window of time.