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Random Recursive Trees and the Bolthausen-Sznitman Coalesent

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Random Recursive Trees and the Bolthausen-Sznitman Coalesent
2.	Creator	Author's name, affiliation, country	Christina Goldschmidt; Statistical Laboratory and Pembroke College, University of Cambridge, UK
2.	Creator	Author's name, affiliation, country	James B. Martin; CNRS and Université Paris 7, France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	We describe a representation of the Bolthausen-Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the coalescent restricted to $[n]$: we show that the distribution of the number of blocks involved in the final collision converges as $n\to\infty$, and obtain a scaling law for the sizes of these blocks. We also consider the discrete-time Markov chain giving the number of blocks after each collision of the coalescent restricted to $[n]$; we show that the transition probabilities of the time-reversal of this Markov chain have limits as $n\to\infty$. These results can be interpreted as describing a ``post-gelation'' phase of the Bolthausen-Sznitman coalescent, in which a giant cluster containing almost all of the mass has already formed and the remaining small blocks are being absorbed.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2005-07-14
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/265
10.	Identifier	Digital Object Identifier	10.1214/EJP.v10-265
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 10
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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