Tightness for branching random walk in a space-inhomogeneous random environment

Abstract

We consider the maximum Mt of branching random walk in a space-inhomogeneous random environment on Z. In this model the branching rate while at some location x∈Z is randomized in an i.i.d. manner. We prove that there is a centering m˜t depending only on the environment such that (Mt−m˜t)t≥0 is tight in an annealed sense.