SPINAL PARTITIONS AND INVARIANCE UNDER RE-ROOTING OF CONTINUUM RANDOM TREES
We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson-Dirichlet family of continuous fragmentation trees...
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| Format: | Journal article |
| Language: | English |
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2009
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| _version_ | 1826264190065573888 |
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| author | Haas, B Pitman, J Winkel, M |
| author_facet | Haas, B Pitman, J Winkel, M |
| author_sort | Haas, B |
| collection | OXFORD |
| description | We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson-Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coarse one by shattering each of its parts independently, according to the same law. As a second application of spinal decompositions, we prove that among the continuous fragmentation trees, stable trees are the only ones whose distribution is invariant under uniform re-rooting. © Institute of Mathematical Statistics, 2009. |
| first_indexed | 2024-03-06T20:03:45Z |
| format | Journal article |
| id | oxford-uuid:2839db63-5347-4592-8e28-bff9e7109d2c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:03:45Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:2839db63-5347-4592-8e28-bff9e7109d2c2022-03-26T12:11:36ZSPINAL PARTITIONS AND INVARIANCE UNDER RE-ROOTING OF CONTINUUM RANDOM TREESJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2839db63-5347-4592-8e28-bff9e7109d2cEnglishSymplectic Elements at Oxford2009Haas, BPitman, JWinkel, MWe develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson-Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coarse one by shattering each of its parts independently, according to the same law. As a second application of spinal decompositions, we prove that among the continuous fragmentation trees, stable trees are the only ones whose distribution is invariant under uniform re-rooting. © Institute of Mathematical Statistics, 2009. |
| spellingShingle | Haas, B Pitman, J Winkel, M SPINAL PARTITIONS AND INVARIANCE UNDER RE-ROOTING OF CONTINUUM RANDOM TREES |
| title | SPINAL PARTITIONS AND INVARIANCE UNDER RE-ROOTING OF CONTINUUM RANDOM TREES |
| title_full | SPINAL PARTITIONS AND INVARIANCE UNDER RE-ROOTING OF CONTINUUM RANDOM TREES |
| title_fullStr | SPINAL PARTITIONS AND INVARIANCE UNDER RE-ROOTING OF CONTINUUM RANDOM TREES |
| title_full_unstemmed | SPINAL PARTITIONS AND INVARIANCE UNDER RE-ROOTING OF CONTINUUM RANDOM TREES |
| title_short | SPINAL PARTITIONS AND INVARIANCE UNDER RE-ROOTING OF CONTINUUM RANDOM TREES |
| title_sort | spinal partitions and invariance under re rooting of continuum random trees |
| work_keys_str_mv | AT haasb spinalpartitionsandinvarianceunderrerootingofcontinuumrandomtrees AT pitmanj spinalpartitionsandinvarianceunderrerootingofcontinuumrandomtrees AT winkelm spinalpartitionsandinvarianceunderrerootingofcontinuumrandomtrees |