Coarsening dynamics of zero-range processes

TL;DR

This paper analyzes the coarsening dynamics of zero-range processes with a condensation transition, emphasizing the importance of finite-time corrections at criticality and in the condensed phase.

Contribution

It provides an analytical study of the coarsening behavior of zero-range processes with faster-than-power-law decay in the stationary state, highlighting finite-time effects.

Findings

Finite-time corrections are crucial for understanding the approach to scaling.

The dynamics differ from power-law decay cases, especially at criticality.

Analytical results are obtained for the complete graph setting.

Abstract

We consider a class of zero-range processes exhibiting a condensation transition in the stationary state, with a critical single-site distribution decaying faster than a power law. We present the analytical study of the coarsening dynamics of the system on the complete graph, both at criticality and in the condensed phase. In contrast with the class of zero-range processes with critical single-site distribution decaying as a power law, in the present case the role of finite-time corrections are essential for the understanding of the approach to scaling.