From urn models to zero-range processes: statics and dynamics

TL;DR

This paper provides a comprehensive overview of zero-range processes, focusing on their static properties and dynamic behavior, especially the condensation transition phenomenon, through conceptual analysis and model study.

Contribution

It offers a detailed analysis of zero-range processes, highlighting the conditions leading to condensation transitions, and synthesizes existing knowledge with new insights.

Findings

Identification of conditions for condensation transition

Analysis of static and dynamic properties of zero-range processes

Insights into related models and their behaviors

Abstract

The aim of these lecture notes is a description of the statics and dynamics of zero-range processes and related models. After revisiting some conceptual aspects of the subject, emphasis is then put on the study of the class of zero-range processes for which a condensation transition arises.