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A branching random walk with a barrier. (English) Zbl 0749.60076
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.

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60G50 Sums of independent random variables; random walks
60F10 Large deviations
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