A new combinatorial representation of the additive coalescent

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...

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Detalles Bibliográficos
Publicado: 2019
Materias:
additive coalescent
Cayley trees
increasing trees
parking
random walks on trees
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10429832_v54_n2_p340_Marckert
http://hdl.handle.net/20.500.12110/paper_10429832_v54_n2_p340_Marckert
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_10429832_v54_n2_p340_Marckert
record_format dspace
spelling paper:paper_10429832_v54_n2_p340_Marckert2023-06-08T16:01:00Z A new combinatorial representation of the additive coalescent additive coalescent Cayley trees increasing trees parking random walks on trees 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. © 2018 Wiley Periodicals, Inc. 2019 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10429832_v54_n2_p340_Marckert http://hdl.handle.net/20.500.12110/paper_10429832_v54_n2_p340_Marckert
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic additive coalescent
Cayley trees
increasing trees
parking
random walks on trees
spellingShingle additive coalescent
Cayley trees
increasing trees
parking
random walks on trees
A new combinatorial representation of the additive coalescent
topic_facet additive coalescent
Cayley trees
increasing trees
parking
random walks on trees
description 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. © 2018 Wiley Periodicals, Inc.
title A new combinatorial representation of the additive coalescent
title_short A new combinatorial representation of the additive coalescent
title_full A new combinatorial representation of the additive coalescent
title_fullStr A new combinatorial representation of the additive coalescent
title_full_unstemmed A new combinatorial representation of the additive coalescent
title_sort new combinatorial representation of the additive coalescent
publishDate 2019
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10429832_v54_n2_p340_Marckert
http://hdl.handle.net/20.500.12110/paper_10429832_v54_n2_p340_Marckert
_version_ 1768545703363084288

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