The cut-and-paste process
  We characterize the class of exchangeable Feller processes evolving on partitions with boundedly many blocks. In continuous-time, the jump measure decomposes into two parts: a $\sigma$-finite measure on stochastic matrices and a collection of nonnegative real constants. This decomposition prompts a L\'evy-It\^o representation. In discrete-time, the evolution is described more simply by a product of independent, identically distributed random matrices. 
Harry Crane
math.PR