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arXiv · 1302.4084

Branching Random Walk in an inhomogeneous breeding potential

Sergey Bocharov·Simon C. Harris
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Abstract

We consider a continuous-time branching random walk in the inhomogeneous breeding potential $\beta|.|^p$, where $\beta > 0$, $p \geq 0$. We prove that the population almost surely explodes in finite time if $p > 1$ and doesn't explode if $p \leq 1$. In the non-explosive cases, we determine the asymptotic behaviour of the rightmost particle.

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Sergey Bocharov, Simon C. Harris. 2013-02-17. Branching Random Walk in an inhomogeneous breeding potential. https://arxiv.org/abs/1302.4084

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