The precise tail behavior of the total progeny of a killed branching random walk

Abstract

Consider a branching random walk on the real line with a killing barrier at zero: starting from a nonnegative point, particles reproduce and move independently, but are killed when they touch the negative half-line. The population of the killed branching random walk dies out almost surely in both critical and subcritical cases, where by subcritical case we mean that the rightmost particle of the branching random walk without killing has a negative speed, and by critical case, when this speed is zero. We investigate the total progeny of the killed branching random walk and give their precise tail distribution both in the critical and subcritical cases, which solves an open problem of Aldous [Power laws and killed branching random walks, http://www.stat.berkeley.edu/~aldous/Research/OP/brw.html].

Published in at http://dx.doi.org/10.1214/13-AOP842 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• The genealogy of branching Brownian motion with absorption
• Minima in branching random walks
• The number of absorbed individuals in branching Brownian motion with a barrier

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