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 |
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2007
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| _version_ | 1797083987315785728 |
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| author | Goldschmidt, C Martin, J Spanò, D |
| author_facet | Goldschmidt, C Martin, J Spanò, D |
| author_sort | Goldschmidt, C |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T01:49:17Z |
| format | Journal article |
| id | oxford-uuid:9983c735-960c-4cfb-96e3-64ce0486f4ce |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:49:17Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:9983c735-960c-4cfb-96e3-64ce0486f4ce2022-03-27T00:14:53ZFragmenting random permutationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9983c735-960c-4cfb-96e3-64ce0486f4ceEnglishSymplectic Elements at Oxford2007Goldschmidt, CMartin, JSpanò, DProblem 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. |
| spellingShingle | Goldschmidt, C Martin, J Spanò, D Fragmenting random permutations |
| title | Fragmenting random permutations |
| title_full | Fragmenting random permutations |
| title_fullStr | Fragmenting random permutations |
| title_full_unstemmed | Fragmenting random permutations |
| title_short | Fragmenting random permutations |
| title_sort | fragmenting random permutations |
| work_keys_str_mv | AT goldschmidtc fragmentingrandompermutations AT martinj fragmentingrandompermutations AT spanod fragmentingrandompermutations |