We consider a continuous-time branching random walk in the inhomogeneous breeding potential β│ │p, where β > 0, p ≥ 0. We prove that the population almost surely explodes in finite time if p > 1 and doesn’t explode if p ≤ 1. In the non-explosive cases, we determine the asymptotic behaviour of the rightmost particle.
CITATION STYLE
Bocharov, S., & Harris, S. C. (2014). Branching random walk in an inhomogeneous breeding potential. Lecture Notes in Mathematics, 2123, 1–32. https://doi.org/10.1007/978-3-319-11970-0_1
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