Biggins, J. D.; Lubachevsky, Boris D.; Schwartz, Adam; Weiss, Alan A branching random walk with a barrier. (English) Zbl 0749.60076 Ann. Appl. Probab. 1, No. 4, 573-581 (1991). A supercritical branching random walk with independent displacements having negative mean is equipped with a left-hand barrier which annihilates individuals which would otherwise pass through it. A simple criterion is obtained for the population to die out with probability one. Under this condition the expected total population size is found to grow asymptotically exponentially, with a determinable rate, as the barrier recedes. The motivation for this study is an interesting application to rollback-based simulation of systems with a large number of components. Reviewer: D.R.Grey (Sheffield) Cited in 1 ReviewCited in 17 Documents MSC: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60G50 Sums of independent random variables; random walks 60F10 Large deviations Keywords:supercritical branching random walk; systems with a large number of components PDFBibTeX XMLCite \textit{J. D. Biggins} et al., Ann. Appl. Probab. 1, No. 4, 573--581 (1991; Zbl 0749.60076) Full Text: DOI