Open Access
2008 Fragmenting random permutations
Christina Goldschmidt, James Martin, Dario Spano
Author Affiliations +
Electron. Commun. Probab. 13: 461-474 (2008). DOI: 10.1214/ECP.v13-1402


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.


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Christina Goldschmidt. James Martin. Dario Spano. "Fragmenting random permutations." Electron. Commun. Probab. 13 461 - 474, 2008.


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

zbMATH: 1189.60022
MathSciNet: MR2430713
Digital Object Identifier: 10.1214/ECP.v13-1402

Primary: 60C05
Secondary: 05A18

Keywords: Chinese restaurant process , Fragmentation process , Gibbs partition , random permutation

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