Branch merging on continuum trees with applications to regenerative tree growth
We introduce a family of branch merging operations on continuum trees and show that Ford CRTs are distributionally invariant. This operation is new even in the special case of the Brownian CRT, which we explore in more detail. The operations are based on spinal decompositions and a regenerativity pr...
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| Format: | Journal article |
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Instituto Nacional de Matemática Pura e Aplicada
2016
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| _version_ | 1826305922143617024 |
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| author | Rembart, F |
| author_facet | Rembart, F |
| author_sort | Rembart, F |
| collection | OXFORD |
| description | We introduce a family of branch merging operations on continuum trees and show that Ford CRTs are distributionally invariant. This operation is new even in the special case of the Brownian CRT, which we explore in more detail. The operations are based on spinal decompositions and a regenerativity preservingmerging procedure of (α; θ)-strings of beads, that is, random intervals [0; Lα;θ] equipped with a random discrete measure dL^-1 arising in the limit of ordered (α; θ)-Chinese restaurant processes as introduced by Pitman and Winkel. Indeed, we iterate the branch merging operation recursively and give a new approach to the leaf embedding problem on Ford CRTs related to (α; 2 - θ)-tree growth processes. |
| first_indexed | 2024-03-07T06:40:09Z |
| format | Journal article |
| id | oxford-uuid:f8fed37a-27a5-462b-9fd0-181f5019c890 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:40:09Z |
| publishDate | 2016 |
| publisher | Instituto Nacional de Matemática Pura e Aplicada |
| record_format | dspace |
| spelling | oxford-uuid:f8fed37a-27a5-462b-9fd0-181f5019c8902022-03-27T12:54:41ZBranch merging on continuum trees with applications to regenerative tree growthJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f8fed37a-27a5-462b-9fd0-181f5019c890Symplectic Elements at OxfordInstituto Nacional de Matemática Pura e Aplicada2016Rembart, FWe introduce a family of branch merging operations on continuum trees and show that Ford CRTs are distributionally invariant. This operation is new even in the special case of the Brownian CRT, which we explore in more detail. The operations are based on spinal decompositions and a regenerativity preservingmerging procedure of (α; θ)-strings of beads, that is, random intervals [0; Lα;θ] equipped with a random discrete measure dL^-1 arising in the limit of ordered (α; θ)-Chinese restaurant processes as introduced by Pitman and Winkel. Indeed, we iterate the branch merging operation recursively and give a new approach to the leaf embedding problem on Ford CRTs related to (α; 2 - θ)-tree growth processes. |
| spellingShingle | Rembart, F Branch merging on continuum trees with applications to regenerative tree growth |
| title | Branch merging on continuum trees with applications to regenerative tree growth |
| title_full | Branch merging on continuum trees with applications to regenerative tree growth |
| title_fullStr | Branch merging on continuum trees with applications to regenerative tree growth |
| title_full_unstemmed | Branch merging on continuum trees with applications to regenerative tree growth |
| title_short | Branch merging on continuum trees with applications to regenerative tree growth |
| title_sort | branch merging on continuum trees with applications to regenerative tree growth |
| work_keys_str_mv | AT rembartf branchmergingoncontinuumtreeswithapplicationstoregenerativetreegrowth |