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

TL;DR

This paper analyzes how quenched disorder affects the condensation transition in the zero-range process, revealing changes in critical behavior and fluctuations in local densities.

Contribution

It provides a rigorous probabilistic analysis of disorder effects on the condensation transition in the zero-range process, highlighting altered critical exponents and density fluctuations.

Findings

Disorder changes the critical exponent for condensation.

Local critical densities exhibit large fluctuations.

Distribution of densities shows exponential to algebraic crossover.

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.