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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 44 open journal systems 


Fragmenting random permutations

Christina Goldschmidt, Department of Statistics, University of Oxford
James B Martin, Department of Statistics, University of Oxford
Dario Spano, Department of Statistics, University of Warwick


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


Full text: PDF

Pages: 461-474

Published on: August 14, 2008
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Electronic Communications in Probability. ISSN: 1083-589X