@article{Lv2023, 
author = {You Lv},
title = {Asymptotic behavior of survival probability for a branching random walk with a barrier},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {2},
pages = {5049-5059},
keywords = {survival probability, barrier, branching random walk},
url = {https://www.sciopen.com/article/10.3934/math.2023253},
doi = {10.3934/math.2023253},
abstract = {Consider a branching random walk with a mechanism of elimination. We assume that the underlying Galton-Watson process is supercritical, thus the branching random walk has a positive survival probability. A mechanism of elimination, which is called a barrier, is introduced to erase the particles who lie above    r  i  +  ε      i          α       and all their descendants, where    i presents the generation of the particles,    α  >  1      /    3  ,  ε  ∈                    R             and    r is the asymptotic speed of the left-most position of the branching random walk. First we show that the particle system still has a positive survival probability after we introduce the barrier with    ε  >  0. Moreover, we show that the decay of the probability is faster than        e          −              β        ′                    ε                  β                     as    ε  ↓  0, where        β    ′    ,  β are two positive constants depending on the branching random walk and    α. The result in the present paper extends a conclusion in Gantert et al. (2011) in some extent. Our proof also works for some time-inhomogeneous cases.}
}