Universality in a class of fragmentation-coalescence processes

Andreas E. Kyprianou, Steven W. Pagett, Timothy Rogers

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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 a universal cluster size distribution regardless of the details of the rates, following a power law with exponent 3/2.
Original languageEnglish
Pages (from-to)1134-1151
Number of pages18
JournalAnnales de l'Institut Henri Poincaré: Probabilités et Statistiques
Issue number2
Publication statusPublished - 1 May 2018


  • Cluster distribution
  • Fragmentation-coalescence
  • Thermodynamic limit

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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