Fragmenting random permutations
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 permutati...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2007
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| Summary: | 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. |
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