A new combinatorial representation of the additive coalescent

Marckert, Jean-François and Wang, Minmin (2019) A new combinatorial representation of the additive coalescent. Random Structures and Algorithms, 54 (2). pp. 340-370. ISSN 1042-9832

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Depositing User: Minmin Wang
Date Deposited: 12 Feb 2019 12:57
Last Modified: 01 Jul 2019 17:15
URI: http://sro.sussex.ac.uk/id/eprint/81913

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