Universality in a class of fragmentation-coalescence processes

TL;DR

This paper studies a class of particle systems where clusters merge and break apart, revealing that under certain conditions, the cluster size distribution becomes deterministic and exhibits universal critical behavior with an exponent of 3/2.

Contribution

It introduces a new class of fragmentation-coalescence processes and demonstrates their universal critical behavior in the thermodynamic limit.

Findings

Cluster size distribution becomes deterministic in the limit.

Processes exhibit self-organised criticality with a universal exponent 3/2.

Universal behavior holds under mild conditions on coalescence rates.

Abstract

We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while fragmentation breaks up a cluster into a collection of singletons. Under mild conditions on the coalescence rates, we show that the distribution of cluster sizes becomes non- random in the thermodynamic limit. Moreover, we discover that in the limit of small fragmentation rate these processes exhibit self-organised criticality in the cluster size distribution, with universal exponent 3/2.