Extremal Process of Last Progeny Modified Branching Random Walks

Partha Pratim Ghosh, Bastien Mallein

Published 2024-05-19Version 1

We consider a last progeny modified branching random walk, in which the position of each particle at the last generation $n$ is modified by an i.i.d. copy of a random variable $Y$. Depending on the asymptotic properties of the tail of $Y$, we describe the asymptotic behaviour of the extremal process of this model as $n \to \infty$.