2012/12/25 by Götz Kersting, Kersting, Götz, Iulia Stanciu +3
Mathematics · #60F05 #60J10 #60K35 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F05 #msc:60J10 #msc:60K35
paper · pdf · doi:10.48550/arxiv.1212.6070
17 pages, 2 figures
arxiv created 2012/12/25 · arxiv updated 2012/12/27
For 1<α<2 we derive the asymptotic distribution of the total length of \em external branches of a Beta(2-α, α)-coalescent as the number n of leaves becomes large. It turns out the fluctuations of the external branch length follow those of τn2-α over the entire parameter regime, where τn denotes the random number of coalescences that bring the n lineages down to one. This is in contrast to the fluctuation behavior of the total branch length, which exhibits a transition at α0 = (1+√ 5)/2.