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2012 Dynamics of the evolving Bolthausen-Sznitman coalecent
Jason Schweinsberg
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Electron. J. Probab. 17: 1-50 (2012). DOI: 10.1214/EJP.v17-2378

Abstract

Consider a population of fixed size that evolves over time. At each time, the genealogical structure of the population can be described by a coalescent tree whose branches are traced back to the most recent common ancestor of the population. As time goes forward, the genealogy of the population evolves, leading to what is known as an evolving coalescent. We will study the evolving coalescent for populations whose genealogy can be described by the Bolthausen Sznitman coalescent. We obtain the limiting behavior of the evolution of the time back to the most recent common ancestor and the total length of the branches in the tree. By similar methods, we also obtain a new result concerning the number of blocks in the Bolthausen-Sznitman coalescent.

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Jason Schweinsberg. "Dynamics of the evolving Bolthausen-Sznitman coalecent." Electron. J. Probab. 17 1 - 50, 2012. https://doi.org/10.1214/EJP.v17-2378

Information

Accepted: 16 October 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1284.92072
MathSciNet: MR2988406
Digital Object Identifier: 10.1214/EJP.v17-2378

Subjects:
Primary: 60J25
Secondary: 60G10, 60G52, 60G55, 92D25

JOURNAL ARTICLE
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Vol.17 • 2012
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