Condensation of Non-Reversible Zero-Range Processes

TL;DR

This paper analyzes the condensation phenomena in non-reversible zero-range processes, establishing new bounds and frameworks to understand metastability and the behavior of condensed sites as Markov chains.

Contribution

It introduces a novel capacity inequality and a robust framework for analyzing metastability in non-reversible zero-range processes, extending previous reversible and asymmetric cases.

Findings

Condensed site behaves as a Markov chain on the underlying graph.

Capacity bounds are established for non-reversible processes.

Results generalize previous work on reversible and asymmetric zero-range processes.

Abstract

In this article, we investigate the condensation phenomena for a class of nonreversible zero-range processes on a fixed finite set. By establishing a novel inequality bounding the capacity between two sets, and by developing a robust framework to perform quantitative analysis on the metastability of non-reversible processes, we prove that the condensed site of the corresponding zero-range processes approximately behaves as a Markov chain on the underlying graph whose jump rate is proportional to the capacity with respect to the underlying random walk. The results presented in the current paper complete the generalization of the work of Beltran and Landim [4] on reversible zero-range processes, and that of Landim [22] on totally asymmetric zero-range processes on a one-dimensional discrete torus.