A note on stable point processes occurring in branching Brownian motion

Pascal Maillard

We call a point process $Z$ on $\mathbb{R}$ \emph{exp-1-stable} if for every $\alpha ,\beta \in \mathbb{R}$ with $e^{\alpha }+e^{\beta }=1$, $Z$ is equal in law to $T_{\alpha }Z+T_{\beta }{Z}^{\prime }$, where $Z^{\prime }$ is an independent co…