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  • On the Height and Length of the Ancestral Recombination Graph

  • Part of
  • Etienne Pardoux, Majid Salamat
  • Journal:
    Journal of Applied Probability / Volume 46 / Issue 3 / September 2009
    Published online by Cambridge University Press:
    14 July 2016, pp. 669-689
    Print publication:
    September 2009
    • Article
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  • 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.