RT Journal Article
SR Electronic
T1 Site Frequency Spectrum of the Bolthausen-Sznitman Coalescent
JF bioRxiv
FD Cold Spring Harbor Laboratory
SP 799627
DO 10.1101/799627
A1 Götz Kersting
A1 Arno Siri-Jégousse
A1 Alejandro H. Wences
YR 2019
UL http://biorxiv.org/content/early/2019/10/10/799627.abstract
AB We derive explicit formulas for the two first moments of he site frequency spectrum (SFSn,b)1≤b≤n−1 of the Bolthausen-Sznitman coalescent along with some precise and efficient approximations, even for small sample sizes n. These results provide new L2-asymptotics for some values of b = o(n). We also study the length of internal branches carrying b > n/2 individuals. In this case we obtain the distribution function and a convergence in law. Our results rely on the random recursive tree construction of the Bolthausen-Sznitman coalescent.