Exchangeable Fragmentation-Coalescence Processes and their Equilibrium Measures
Julien Berestycki, université de Provence, France
Abstract
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 Möhle 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.
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