Fragmenting random permutations
Probability
2007-12-05 v1 Combinatorics
Abstract
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) taking values in the space of partitions of {1,2,...,n} such that \Pi_{n,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.
Cite
@article{arxiv.0712.0556,
title = {Fragmenting random permutations},
author = {Christina Goldschmidt and James B. Martin and Dario Spanò},
journal= {arXiv preprint arXiv:0712.0556},
year = {2007}
}
Comments
13 pages, 3 figures