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Reference: Rembart, F, (2016). Branch merging on continuum trees with applications to regenerative tree growth. Latin American Journal of Probability and Mathematical Statistics.Citable link to this page:

 

Branch merging on continuum trees with applications to regenerative tree growth

Abstract: 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.

Peer Review status:Peer reviewedPublication status:PublishedVersion:Publisher's versionNotes:© 2016 Franz Rembart. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs.

Bibliographic Details

Publisher: Instituto Nacional de Matemática Pura e Aplicada

Publisher Website: http://www.impa.br/

Publisher: Instituto Nacional de Matemática Pura e Aplicada

Journal: Latin American Journal of Probability and Mathematical Statisticssee more from them

Publication Website: http://alea.impa.br/

Issue Date: 2016-06

Article Number:Identifiers

Urn: uuid:f8fed37a-27a5-462b-9fd0-181f5019c890

Source identifier: 633422

Issn: 1980-0436 Item Description

Type: Journal article;

Version: Publisher's versionKeywords: String of beads Chinese restaurant process regenerative interval partition Poisson-Dirichlet Ford CRT Brownian CRT branch merging tree-valued Markov process Tiny URL: pubs:633422

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Author: Rembart, F - institutionUniversity of Oxford Oxford, MPLS, Statistics grantNumberEP-P505666-1 fundingEngineering and Physical Sci

Source: https://ora.ox.ac.uk/objects/uuid:f8fed37a-27a5-462b-9fd0-181f5019c890



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