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A new combinatorial representation of the additive coalescent
- Source :
- Random Structures and Algorithms, Random Structures and Algorithms, Wiley, 2019, 54 (2), pp.340-370. ⟨10.1002/rsa.20775⟩
- Publication Year :
- 2018
- Publisher :
- Wiley, 2018.
-
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 & Louchard as the block sizes in a parking scheme. In the coalescent forest representation, some edges are added successively between a random node and a random root. In this paper, we investigate an alternative construction by adding edges between the roots. This construction induces the same process at the level of cluster sizes, but allows one to make numerous connections with some combinatorial and probabilistic models that were not known to be connected with additive coalescent. The variety of the combinatorial objects involved here – size biased percolation, parking scheme in a tree, increasing trees, random cuts of trees – justifies our interests in this Acknowledgement : The research has been supported by ANR-14-CE25-0014 (ANR GRAAL).
- Subjects :
- [MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
parking
General Mathematics
68R05 Key Words: additive coalescent
Markov process
0102 computer and information sciences
01 natural sciences
increasing trees
Coalescent theory
Combinatorics
symbols.namesake
60J25
60F05
Representation (mathematics)
ComputingMilieux_MISCELLANEOUS
construction Mathematics Subject Classification (2000) 60C05
Mathematics
Block (data storage)
Discrete mathematics
Applied Mathematics
Probabilistic logic
Cayley trees
Computer Graphics and Computer-Aided Design
Tree (graph theory)
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
random walks on trees
60K35
010201 computation theory & mathematics
symbols
Node (circuits)
Variety (universal algebra)
Software
Subjects
Details
- ISSN :
- 10429832 and 10982418
- Volume :
- 54
- Database :
- OpenAIRE
- Journal :
- Random Structures & Algorithms
- Accession number :
- edsair.doi.dedup.....67a50a2b5659fa4501ef396751bd2698