Branching random walk in an inhomogeneous breeding potential

Sergey Bocharov; Simon C. Harris

doi:10.1007/978-3-319-11970-0_1

Branching random walk in an inhomogeneous breeding potential

Sergey Bocharov, Simon C. Harris^*

^*Corresponding author for this work

University of Bath, Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1-32
Number of pages	32
Journal	Lecture Notes in Mathematics
Volume	2123
DOIs	https://doi.org/10.1007/978-3-319-11970-0_1
Publication status	Published - 2014
Externally published	Yes

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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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N2 - 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.

AB - 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.

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Branching random walk in an inhomogeneous breeding potential

Abstract

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