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A new combinatorial representation of the additive coalescent

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posted on 2023-06-09, 16:51 authored by Jean-François Marckert, Minmin WangMinmin Wang
The 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 Algorithms

ISSN

1042-9832

Publisher

Wiley

Issue

2

Volume

54

Page range

340-370

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-02-12

First Open Access (FOA) Date

2019-04-02

First Compliant Deposit (FCD) Date

2019-02-11

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