Exchangeable Fragmentation-Coalescence Processes and their Equilibrium Measures

By J. Berestycki. 2004

51 citations recorded by the source corpus.

We define and study a family of Markov processes with state space the compact set of all partitions of $N$ that we call exchangeable fragmentation-coalescence processes. They can be viewed as a combination of homogeneous fragmentation as defined by Bertoin and of homogenous coalescence as defined by Pitman and Schweinsberg or Mohle and Sagitov. We show that they admit a unique invariant probability measure and we study some properties of their paths and of their equilibrium measure.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9eda0e98e8f5472f9f5d0989890874f369fe562d

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

The branching process with logistic growth (2005, background): “In [4], all exchangeable coalescence-fragmentation (EFC) processes living in the partitions ofN are characterized.”
Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process (2005, background): “process (see Introduction) whose sudden dislocations do not create dust, having parameters (according to the notations of [3]): ck = 0, ce = 1 νcoag(dy) = f 3 2 , 1 2 (y)dy.”
Combinatorial Stochastic Processes (2006, methodology): “Berestycki [36] considers exchangeable coalescent-fragmentations in equilibrium, providing a synthesis of the works by Schweinsberg and Bertoin.”