Abstract
We consider branching random walk in random environment (BRWRE) and prove the existence of deterministic subsequences along which their maximum, centered at its mean, is tight. This partially answers an open question in [3]. The method of proof adapts an argument developed by Dekking and Host for branching random walks with bounded increments. The question of tightness without the need for subsequences remains open.
Funding Statement
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 692452).
Acknowledgments
Thanks to Ofer Zeitouni for suggesting the problem and for many useful discussions.
Thanks also to Alexander Drewitz, Jiří Černý and an anonymous referee for suggesting the extension to the quenched setup.
Citation
Xaver Kriechbaum. "Subsequential tightness for branching random walk in random environment." Electron. Commun. Probab. 26 1 - 12, 2021. https://doi.org/10.1214/21-ECP386
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