Zheng, Xinghua - In: Stochastic Processes and their Applications 120 (2010) 9, pp. 1821-1836
We study critical branching random walks (BRWs) U(n) on where the displacement of an offspring from its parent has drift towards the origin and reflection at the origin. We prove that for any [alpha]1, conditional on survival to generation [n[alpha]], the maximal displacement is ....