The cut-and-paste process

Abstract

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 $σ$-finite measure on stochastic matrices and a collection of nonnegative real constants. This decomposition prompts a Lévy-Itô representation. In discrete-time, the evolution is described more simply by a product of independent, identically distributed random matrices.

Published in at http://dx.doi.org/10.1214/14-AOP922 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)