Branch merging on continuum trees with applications to regenerative tree growth

Journal article

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.

Authors: Rembart, F

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Instituto Nacional de Matemática Pura e Aplicada
• Journal: Latin American Journal of Probability and Mathematical Statistics
• Volume: 13
• Issue: 2
• Pages: 563-603
• Publication date: 2016-06-01
• Acceptance date: 2016-04-25
• DOI: 10.30757/ALEA.v13-23
• ISSN: 1980-0436
• Language: English
• Keywords: tree-valued Markov process; Chinese restaurant process; Ford CRT; Brownian CRT; Poisson-Dirichlet; branch merging; regenerative interval partition; string of beads