Universality in a class of fragmentation-coalescence processes

Andreas E. Kyprianou; Steven W. Pagett; Tim Rogers

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arXiv · 1504.03196

Universality in a class of fragmentation-coalescence processes

Andreas E. Kyprianou·Steven W. Pagett·Tim Rogers

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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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Andreas E. Kyprianou, Steven W. Pagett, Tim Rogers. 2015-04-13. Universality in a class of fragmentation-coalescence processes. https://arxiv.org/abs/1504.03196

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