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

1 Citation (Scopus)

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

Access to Document

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

Cite this

@article{8d57ecd531bf45968f960679fe7d6726,

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.\}",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2014.",

year = "2014",

doi = "10.1007/978-3-319-11970-0\_1",

language = "English",

volume = "2123",

pages = "1--32",

journal = "Lecture Notes in Mathematics",

issn = "0075-8434",

}

TY - JOUR

T1 - Branching random walk in an inhomogeneous breeding potential

AU - Bocharov, Sergey

AU - Harris, Simon C.

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2014.

PY - 2014

Y1 - 2014

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

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

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

M3 - Article

AN - SCOPUS:84926679217

SN - 0075-8434

VL - 2123

SP - 1

EP - 32

JO - Lecture Notes in Mathematics

JF - Lecture Notes in Mathematics

ER -

Branching random walk in an inhomogeneous breeding potential

Abstract

Access to Document

Other files and links

Fingerprint

Cite this