In this paper we study the existence phase transition of the random fractal ball model and the random fractal box model. We show that both of these are in the empty phase at the critical point of this phase transition.
"The existence phase transition for two Poisson random fractal models." Electron. Commun. Probab. 22 1 - 8, 2017. https://doi.org/10.1214/17-ECP52