The largest fragment of a homogeneous fragmentation process

Andreas Kyprianou, Francis Lane, Peter Mörters

We show that in homogeneous fragmentation processes the largest fragment at time $t$ has size $e^{-t{\Phi }^{\prime }(\bar{p})}{t}^{-\frac{3}{2}(\log \Phi {)}^{\prime }(\bar{p})+o(1)},$ where $\Phi$ is the Lévy expone…