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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10429832_v54_n2_p340_Marckert |
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todo:paper_10429832_v54_n2_p340_Marckert2023-10-03T15:58:11Z A new combinatorial representation of the additive coalescent Marckert, J.-F. Wang, M. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Marckert, J.-F. Wang, M. 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. |
| format |
JOUR |
| author |
Marckert, J.-F. Wang, M. |
| author_facet |
Marckert, J.-F. Wang, M. |
| author_sort |
Marckert, J.-F. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_10429832_v54_n2_p340_Marckert |
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AT marckertjf anewcombinatorialrepresentationoftheadditivecoalescent AT wangm anewcombinatorialrepresentationoftheadditivecoalescent AT marckertjf newcombinatorialrepresentationoftheadditivecoalescent AT wangm newcombinatorialrepresentationoftheadditivecoalescent |
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1807322473870393344 |