main.tex

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\title{
Phase-Type Distributions for Finite Interacting Particle Systems\\
{\large University of Gothenburg}
}

\author{Stefan Eng\\
    Advisor: Jeff Steif
}
\date{2019/2020}


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\begin{document}

\maketitle

\chapter*{Abstract}
Phase-type distributions represent the absorption time in an absorbing Markov chain with one absorbing state.
We look at the phase-type distributions of the voter model and the contact process on finite graphs.
Exact densities of the phase-type distribution are computed for simple cases and numeric approximations are computed for more complicated cases.
In the complete graph case we derive a formula for the expected value of the absorption time on a graph with $N$ nodes for both the voter model and contact process.
The limiting distribution of the contact process is computed for a fixed sized complete graph as the infection rate goes to infinity.

% \chapter*{Dedication}
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% \chapter*{Declaration}
% I declare that..

% \chapter*{Acknowledgements}
% I want to thank...

\tableofcontents
\clearpage

\chapter{Introduction}
\include{chapters/intro}

\chapter{Background}
\include{chapters/background}

\chapter{Phase-Type distributions}
\include{chapters/phase_type}

\chapter{Voter Model}
\input{chapters/voter}

\chapter{Contact Process}
\include{chapters/contact}

\appendix
\chapter{Appendix}
\input{chapters/appendix}

\clearpage
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\end{document}