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

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	Séminaire de Probabilités
Volume	XLVI
DOIs	https://doi.org/10.1007/978-3-319-11970-0_1
Publication status	Published - 30 Oct 2014

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title = "Branching random walk in an inhomogeneous breeding potential",

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{\textquoteright}t explode if p ≤ 1. In the non-explosive cases, we determine the asymptotic behaviour of the rightmost particle.",

author = "Sergey Bocharov and Harris, \{Simon C.\}",

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AU - Harris, Simon C.

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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.

UR - https://www.scopus.com/pages/publications/84926679217

UR - http://dx.doi.org/10.1007/978-3-319-11970-0_1

U2 - 10.1007/978-3-319-11970-0_1

DO - 10.1007/978-3-319-11970-0_1

M3 - Article

AN - SCOPUS:84926679217

SN - 1721-8766

VL - XLVI

SP - 1

EP - 32

JO - Séminaire de Probabilités

JF - Séminaire de Probabilités

ER -

Branching random walk in an inhomogeneous breeding potential

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