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2015 A mixing tree-valued process arising under neutral evolution with recombination
Andrej Depperschmidt, Étienne Pardoux, Peter Pfaffelhuber
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Electron. J. Probab. 20: 1-22 (2015). DOI: 10.1214/EJP.v20-4286


The genealogy at a single locus of a constant size $N$ population in equilibrium is given by the well-known Kingman's coalescent. When considering multiple loci under recombination, the ancestral recombination graph encodes the genealogies at all loci in one graph. For a continuous genome $\mathbb G$, we study the tree-valued process $(T^N_u)_{u\in\mathbb{G}}$ of genealogies along the genome in the limit $N\to\infty$. Encoding trees as metric measure spaces, we show convergence to a tree-valued process with cadlag paths. In addition, we study mixing properties of the resulting process for loci which are far apart.


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Andrej Depperschmidt. Étienne Pardoux. Peter Pfaffelhuber. "A mixing tree-valued process arising under neutral evolution with recombination." Electron. J. Probab. 20 1 - 22, 2015.


Accepted: 12 September 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1371.92096
MathSciNet: MR3399830
Digital Object Identifier: 10.1214/EJP.v20-4286

Primary: 60G10, 92D15
Secondary: 60K35


Vol.20 • 2015
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