The range of asymmetric branching random walk

We consider a simple branching random walk in which each individual performs an asymmetric random walk on the real line and record the positions of all individuals in each generation. In this paper, we show that the set of occupied positions is eventually an interval almost surely on the event of non-extinction, extending the results of Grill and Johnson.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this paper, we study a simple branching random walk model and show that the set of occupied positions eventually becomes an interval almost surely when the individuals do not go extinct.