On the height and length of the ancestral recombination graph
Pardoux Etienne and Salamat Majid
Source: J. Appl. Probab.
Volume 46, Number 3
(2009), 669-689.
Abstract
The goal of this paper is to provide formulae for the expectation
and variance of the height and length of the ancestral
recombination graph (ARG). While the formula for the expectation
of the height is known (see, e.g. Krone and Neuhauser (1997)), the
other formulae seem to be new. We obtain in particular (see
Theorem 4.1) a very simple formula which expresses the
expectation of the length of the ARG as a linear combination of
the expectations of both the length of the coalescent tree and the
height of the ARG. Finally, we study the speed at which the ARG
comes down from infinity.
Primary Subjects: 60J27
Secondary Subjects: 60G51, 92D10
Keywords: Wright--Fisher model; coalescent; recombination; ancestral recombination graph
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1253279845
Digital Object Identifier: doi:10.1239/jap/1253279845
Zentralblatt MATH identifier:
05611411
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