A branching random walk with a barrier (Q1182685)

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.