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- Title
Coupling Bertoin's and Aldous–Pitman's representations of the additive coalescent.
- Authors
Kortchemski, Igor; Thévenin, Paul
- Abstract
We construct a coupling between two seemingly very different constructions of the standard additive coalescent, which describes the evolution of masses merging pairwise at rates proportional to their sums. The first construction, due to Aldous and Pitman, involves the components obtained by logging the Brownian continuum random tree (CRT) by a Poissonian rain on its skeleton as time increases. The second one, due to Bertoin, involves the excursions above its running infimum of a linear‐drifted standard Brownian excursion as its drift decreases. Our main tool is the use of an exploration algorithm of the so‐called cut‐tree of the Brownian CRT, which is a tree that encodes the genealogy of the fragmentation of the CRT.
- Subjects
ENGINEERING standards; ADDITIVES
- Publication
Random Structures & Algorithms, 2024, Vol 65, Issue 1, p17
- ISSN
1042-9832
- Publication type
Article
- DOI
10.1002/rsa.21206