Poisson Representation of a Ewens Fragmentation Process

Source abstract

A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of [ n ] = 1,. . ., n at time θ ≥ 0 is governed by the Ewens sampling formula with parameter θ. These partition-valued processes are exchangeable and consistent, as n varies. They can be derived by uniform sampling from a corresponding mass fragmentation process defined by cutting a unit interval at the points of a Poisson process with intensity θx −1 d x on/mathbbR + , arranged to beintensifying as θ increases.