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A remark on localization for branching random walks in random environment. (English) Zbl 1225.60158
Summary: 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 has already been proven before by Y. Hu and N. Yoshida [Stochastic Processes Appl. 119, No. 5, 1632–1651 (2009; Zbl 1161.60341)], but it is possible to drop their assumption that particles may not die.

MSC:
60K37 Processes in random environments
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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