We give new formulas on the total number of born particles in the stable birth-and-assassination process, and prove that it has a heavy-tailed distribution. We also establish that this process is a scaling limit of a process of rumor scotching in a network, and is related to a predator-prey dynamics.
Charles Bordenave. "On the birth-and-assassination process, with an application to scotching a rumor in a network." Electron. J. Probab. 13 2014 - 2030, 2008. https://doi.org/10.1214/EJP.v13-573