Instability of condensation in the zero-range process with random interaction

Abstract

The zero-range process is a stochastic interacting particle system that is known to exhibit a condensation transition. We present a detailed analysis of this transition in the presence of quenched disorder in the particle interactions. Using rigorous probabilistic arguments we show that disorder changes the critical exponent in the interaction strength below which a condensation transition may occur. The local critical densities may exhibit large fluctuations and their distribution shows an interesting crossover from exponential to algebraic behaviour.

4 pages, 4 figures; included new simulation data (Fig. 4), small changes in introduction and conclusion

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• Development and regression of a large fluctuation
• Structure of the condensed phase in the inclusion process
• Condensation in randomly perturbed zero-range processes
• Localization, big-jump regime and the effect disorder for a class of generalized pinning models
• Localization for a random walk in slowly decreasing random potential
• Condensate formation in a zero-range process with random site capacities