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A new combinatorial representation of the additive coalescent
journal contribution
posted on 2023-06-09, 16:51 authored by Jean-François Marckert, Minmin WangMinmin WangThe standard additive coalescent starting with n particles is a Markov process which owns several combinatorial representations, one by Pitman as a process of coalescent forests, and one by Chassaing and Louchard as the block sizes in a parking scheme. In the coalescent forest representation, edges are added successively between a random node and a random root. In this paper, we investigate an alternative construction by, instead, adding edges between roots. This construction induces exactly the same process in terms of cluster sizes, meanwhile, it allows us to make numerous new connections with other combinatorial and probabilistic models: size biased percolation, parking scheme in a tree, increasing trees, random cuts of trees. The variety of the combinatorial objects involved justifies our interest in this construction.
History
Publication status
- Published
File Version
- Accepted version
Journal
Random Structures and AlgorithmsISSN
1042-9832Publisher
WileyExternal DOI
Issue
2Volume
54Page range
340-370Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2019-02-12First Open Access (FOA) Date
2019-04-02First Compliant Deposit (FCD) Date
2019-02-11Usage metrics
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