Exchangeable Fragmentation-Coalescence processes and their equilibrium   measures
  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 exchangeable 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. 
Julien Berestycki