Increments of Random Partitions

DOI10.1017/S0963548305007455zbMATH Open1119.60003arXivmath/0310091MaRDI QIDQ5295403

Şerban Nacu

Publication date: 30 July 2007

Published in: Combinatorics, Probability and Computing (Search for Journal in Brave)

Abstract: For any partition of $1,2,...,n$ we define its {it increments} $X_i,1leilen$ by $X_i=1$ if $i$ is the smallest element in the partition block that contains it, $X_i=0$ otherwise. We prove that for partially exchangeable random partitions (where the probability of a partition depends only on its block sizes in order of appearance), the law of the increments uniquely determines the law of the partition. One consequence is that the Chinese Restaurant Process CRP($heta$) (the partition with distribution given by the Ewens sampling formula with parameter $heta$) is the only exchangeable random partition with independent increments.

Full work available at URL: https://arxiv.org/abs/math/0310091

Mathematics Subject Classification ID

Combinatorial probability (60C05)

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