Home > Research > Publications & Outputs > Competition within random growth models

Electronic data

  • 2018turnbullphd

    Final published version, 3.52 MB, PDF document

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

Text available via DOI:

View graph of relations

Competition within random growth models

Research output: ThesisDoctoral Thesis

Published

Standard

Competition within random growth models. / Turnbull, Shane.

Lancaster University, 2018. 94 p.

Research output: ThesisDoctoral Thesis

Harvard

APA

Vancouver

Author

Turnbull, Shane. / Competition within random growth models. Lancaster University, 2018. 94 p.

Bibtex

@phdthesis{0b112c41b6a347c380d831ed07b74b3d,
title = "Competition within random growth models",
abstract = "This thesis is concerned with introducing competition into random models. It can be observed that there are two natural mechanisms for the evolution of a random model; either by growth or by self interactions. What we do is look at two types of models and introduce competition within them. The first model, the voter model, is an example of a self interacting model and we introduce growth into it. The second model, the Hasting-Levitov model, is a random growth model and we introduce competition within the model.In both cases we construct diffusion approximations to model these systems when the initial population is large for the first case and when the addition of incoming particles is small in the second. Once these diffusion processes have been constructed we then analyse the long term behaviour of them and find their asymptotic distribution, this is done by using the speed measure and scale function.",
author = "Shane Turnbull",
year = "2018",
doi = "10.17635/lancaster/thesis/405",
language = "English",
publisher = "Lancaster University",
school = "Lancaster University",

}

RIS

TY - THES

T1 - Competition within random growth models

AU - Turnbull, Shane

PY - 2018

Y1 - 2018

N2 - This thesis is concerned with introducing competition into random models. It can be observed that there are two natural mechanisms for the evolution of a random model; either by growth or by self interactions. What we do is look at two types of models and introduce competition within them. The first model, the voter model, is an example of a self interacting model and we introduce growth into it. The second model, the Hasting-Levitov model, is a random growth model and we introduce competition within the model.In both cases we construct diffusion approximations to model these systems when the initial population is large for the first case and when the addition of incoming particles is small in the second. Once these diffusion processes have been constructed we then analyse the long term behaviour of them and find their asymptotic distribution, this is done by using the speed measure and scale function.

AB - This thesis is concerned with introducing competition into random models. It can be observed that there are two natural mechanisms for the evolution of a random model; either by growth or by self interactions. What we do is look at two types of models and introduce competition within them. The first model, the voter model, is an example of a self interacting model and we introduce growth into it. The second model, the Hasting-Levitov model, is a random growth model and we introduce competition within the model.In both cases we construct diffusion approximations to model these systems when the initial population is large for the first case and when the addition of incoming particles is small in the second. Once these diffusion processes have been constructed we then analyse the long term behaviour of them and find their asymptotic distribution, this is done by using the speed measure and scale function.

U2 - 10.17635/lancaster/thesis/405

DO - 10.17635/lancaster/thesis/405

M3 - Doctoral Thesis

PB - Lancaster University

ER -