On the maximal offspring in a critical branching process with infinite variance
Abstract
We investigate the maximal number $M_k$ of offsprings amongst all individuals in a critical Galton-Watson process started with $k$ ancestors. We show that when the reproduction law has a regularly varying tail with index $-\alpha$ for $1<\alpha<2$, then $k^{-1}M_k$ converges in distribution to a Frechet law with shape parameter $1$ and scale parameter depending only on $\alpha$.
Origin : Files produced by the author(s)
Loading...