EJP Reading Tools

Alpha-Stable Branching and Beta-Coalescents

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Alpha-Stable Branching and Beta-Coalescents
2.	Creator	Author's name, affiliation, country	Matthias Birkner; Weierstrass Institute for Applied Analysis and Stochastics, Germany
2.	Creator	Author's name, affiliation, country	Jochen Blath; University of Oxford, UK
2.	Creator	Author's name, affiliation, country	Marcella Capaldo; University of Oxford, UK
2.	Creator	Author's name, affiliation, country	Alison M. Etheridge; University of Oxford, UK
2.	Creator	Author's name, affiliation, country	Martin Möhle; University of Tübingen, Germany
2.	Creator	Author's name, affiliation, country	Jason Schweinsberg; University of California at San Diego, USA
2.	Creator	Author's name, affiliation, country	Anton Wakolbinger; J. W. Goethe Universität
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	We determine that the continuous-state branching processes for which the genealogy, suitably time-changed, can be described by an autonomous Markov process are precisely those arising from $\alpha$-stable branching mechanisms.  The random ancestral partition is then a time-changed $\Lambda$-coalescent, where $\Lambda$ is the Beta-distribution with parameters $2-\alpha$ and $\alpha$, and the time change is given by $Z^{1-\alpha}$, where $Z$ is the total population size. For $\alpha = 2$ (Feller's branching diffusion) and $\Lambda = \delta_0$ (Kingman's coalescent), this is in the spirit of (a non-spatial version of) Perkins' Disintegration Theorem.  For $\alpha =1$ and $\Lambda$ the uniform distribution on $[0,1]$, this is the duality discovered by Bertoin & Le Gall (2000) between the norming of Neveu's continuous state branching process and the Bolthausen-Sznitman coalescent. We present two approaches: one, exploiting the `modified lookdown construction', draws heavily on Donnelly & Kurtz (1999); the other is based on direct calculations with generators.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2005-03-04
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/241
10.	Identifier	Digital Object Identifier	10.1214/EJP.v10-241
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.)
15.	Rights	Copyright and permissions	The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available. Summary of the Creative Commons Attribution License You are free to copy, distribute, display, and perform the work to make derivative works to make commercial use of the work under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.