Electronic Communications in Probability

Fragmenting random permutations

Christina Goldschmidt, James Martin, and Dario Spano

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Problem 1.5.7 from Pitman's Saint-Flour lecture notes: Does there exist for each $n$ a fragmentation process $(\Pi_{n,k}, 1 \leq k \leq n)$ such that $\Pi_{n,k}$ is distributed like the partition generated by cycles of a uniform random permutation of $\{1,2,\ldots,n\}$ conditioned to have $k$ cycles? We show that the answer is yes. We also give a partial extension to general exchangeable Gibbs partitions.

Article information

Electron. Commun. Probab. Volume 13 (2008), paper no. 44, 461-474.

Accepted: 14 August 2008
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability
Secondary: 05A18: Partitions of sets

Fragmentation process random permutation Gibbs partition Chinese restaurant process

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Goldschmidt, Christina; Martin, James; Spano, Dario. Fragmenting random permutations. Electron. Commun. Probab. 13 (2008), paper no. 44, 461--474. doi:10.1214/ECP.v13-1402. https://projecteuclid.org/euclid.ecp/1465233471

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