Poisson - Kingman Partitions ∗ Jim Pitman

Poisson - Kingman Partitions ∗

This paper presents some general formulas for random partitions of a finite set derived by Kingman’s model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the ...

2 00 2 Poisson - Kingman Partitions ∗

This paper presents some general formulas for random partitions of a finite set derived by Kingman’s model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the ...

Exchangeable and partially exchangeable random partitions

Call a random partition of the positive integers partially exchangeable if for each finite sequence of positive integers n l , . . . , nk, the probability that the partition breaks the first nl + . . . § nk integers into k particular classes, of sizes nl . . . . , nk in order of their first elements, has the same value p(na . . . . . nk) for every possible choice of classes subject to the sizes...

Some Probabilistic Aspects of Set Partitions

Poisson-Dirichlet And Gem Invariant Distributions For Split-And-Merge Transformations Of An Interval Partition

This paper introduces a split-and-merge transformation of interval partitions which combines some features of one model studied by Gnedin and Kerov [12, 11] and another studied by Tsilevich [30, 31] and Mayer-Wolf, Zeitouni and Zerner [21]. The invariance under this split-and-merge transformation of the interval partition generated by a suitable Poisson process yields a simple proof of the rece...