We prove a localization-result for branching random walks in random environment, namely that if the process does not die out, the most populated site will infinitely often contain more than a fixed percentage of the population. This had been proven already before by Hu and Yoshida, but it is possible to drop their assumption that particles may not die.
"A Remark on Localization for Branching Random Walks in Random Environment." Electron. Commun. Probab. 16 323 - 336, 2011. https://doi.org/10.1214/ECP.v16-1603