Exchangeable Fragmentation-Coalescence processes and their equilibrium measures

We define and study a family of Markov processes with state spacethe compact set of all partitions of N that we callexchangeable fragmentation-coalescence processes. They can beviewed as a combination of exchangeable fragmentation as definedby Bertoin and of homogenous coalescence as defined by Pitman andSchweinsberg or Möhle and Sagitov. We show that they admit aunique invariant probability measure and we study some propertiesof their paths and of their equilibrium measure