%0 Journal Article
%T A mixing tree-valued process arising under neutral evolution with recombination
%+ Abteilung für Mathematische Stochastik
%+ Institut de Mathématiques de Marseille (I2M)
%A Depperschmidt, Andrej
%A Pardoux, Étienne
%A Pfaffelhuber, Peter
%< avec comité de lecture
%@ 1083-6489
%J Electronic Journal of Probability
%I Institute of Mathematical Statistics (IMS)
%V 20
%P 1-22
%8 2015-09-12
%D 2015
%Z 1505.01165
%R 10.1214/EJP.v20-4286
%K Ancestral recombination graph
%K Kingman coalescent
%K tree-valued process
%K Gromov-Hausdorff metric
%Z Mathematics [math]
%Z Mathematics [math]/General Mathematics [math.GM]Journal articles
%X 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 G, we study the tree-valued process (T N u)u∈G of genealogies along the genome in the limit N → ∞. Encoding trees as metric measure spaces, we show convergence to a tree-valued process with càdlàg paths. In addition, we study mixing properties of the resulting process for loci which are far apart.
%G English
%2 https://amu.hal.science/hal-01237957/document
%2 https://amu.hal.science/hal-01237957/file/4286-22857-1-PB.pdf
%L hal-01237957
%U https://amu.hal.science/hal-01237957
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-