%0 Generic %1 GPEwens %A Gnedin, Alexander %A Pitman, Jim %D 2006 %K Dept_Mathematics_Berkeley Dept_Statistics_Berkeley Ewens_sampling_formula fragmentation poisson_point_process myown %R 10.1017/S0963548306008352 %T Poisson representation of a Ewens fragmentation process %X A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of $n=1,...,n$ at time $0$ is governed by the Ewens sampling formula with parameter $þeta$. 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 $x^-1 dx$ on $R_+$, arranged to be intensifying as $þeta$ increases.

@misc{GPEwens, abstract = {A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of $[n]={1,...,n}$ at time $\theta \ge 0$ is governed by the Ewens sampling formula with parameter $\theta$. 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 $\theta x^{-1} dx$ on $R_+$, arranged to be intensifying as $\theta$ increases.}, added-at = {2008-01-20T22:46:04.000+0100}, arxiv = {math.PR/0608307}, author = {Gnedin, Alexander and Pitman, Jim}, biburl = {https://www.bibsonomy.org/bibtex/2122a170fd4b4cd5a4fa3acbe91c34afd/pitman}, doi = {10.1017/S0963548306008352}, interhash = {b4af86df6486a758c7faa08972d68656}, intrahash = {122a170fd4b4cd5a4fa3acbe91c34afd}, keywords = {Dept_Mathematics_Berkeley Dept_Statistics_Berkeley Ewens_sampling_formula fragmentation poisson_point_process myown}, note = {to appear in Combinatorics, Probability and Computing}, timestamp = {2010-10-30T22:51:58.000+0200}, title = {{Poisson representation of a Ewens fragmentation process}}, year = 2006 }