Site Frequency Spectrum of the Bolthausen-Sznitman coalescent

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.