We consider branching random walk in 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 arXiv:1711.00852. The method proof adapts argument developed by Dekking Host for walks with bounded increments. tightness without need remains open.

A correction to this paper has been published: 10.1007/s00440-016-0699-z