Universality in a class of fragmentation-coalescence processes

2015/04/13 by Kyprianou, Andreas E., Pagett, Steven W., Rogers, Tim
#60K35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1504.03196

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.

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