Superprocesses and Large-Scale Networks

The main theme of this thesis is the use of the branching property in the analysis of random structures. The thesis consists of two self-contained parts. In the first part, we study the long-term behaviour of supercritical superdiffusions and prove the strong law of large numbers. The key tools are...

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Main Author:	Eckhoff, Maren
Other Authors:	Kyprianou, Andreas ; Morters, Peter
Published:	University of Bath 2014
Subjects:	519.2
Online Access:	https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.675692

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spelling	ndltd-bl.uk-oai-ethos.bl.uk-6756922019-03-14T03:27:19ZSuperprocesses and Large-Scale NetworksEckhoff, MarenKyprianou, Andreas ; Morters, Peter2014The main theme of this thesis is the use of the branching property in the analysis of random structures. The thesis consists of two self-contained parts. In the first part, we study the long-term behaviour of supercritical superdiffusions and prove the strong law of large numbers. The key tools are spine and skeleton decompositions, and the analysis of the corresponding diffusions and branching particle diffusions. In the second part, we consider preferential attachment networks and quantify their vulnerability to targeted attacks. Despite the very involved global topology, locally the network can be approximated by a multitype branching random walk with two killing boundaries. Our arguments exploit this connection.519.2University of Bathhttps://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.675692Electronic Thesis or Dissertation
collection	NDLTD
sources	NDLTD
topic	519.2
spellingShingle	519.2 Eckhoff, Maren Superprocesses and Large-Scale Networks
description	The main theme of this thesis is the use of the branching property in the analysis of random structures. The thesis consists of two self-contained parts. In the first part, we study the long-term behaviour of supercritical superdiffusions and prove the strong law of large numbers. The key tools are spine and skeleton decompositions, and the analysis of the corresponding diffusions and branching particle diffusions. In the second part, we consider preferential attachment networks and quantify their vulnerability to targeted attacks. Despite the very involved global topology, locally the network can be approximated by a multitype branching random walk with two killing boundaries. Our arguments exploit this connection.
author2	Kyprianou, Andreas ; Morters, Peter
author_facet	Kyprianou, Andreas ; Morters, Peter Eckhoff, Maren
author	Eckhoff, Maren
author_sort	Eckhoff, Maren
title	Superprocesses and Large-Scale Networks
title_short	Superprocesses and Large-Scale Networks
title_full	Superprocesses and Large-Scale Networks
title_fullStr	Superprocesses and Large-Scale Networks
title_full_unstemmed	Superprocesses and Large-Scale Networks
title_sort	superprocesses and large-scale networks
publisher	University of Bath
publishDate	2014
url	https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.675692
work_keys_str_mv	AT eckhoffmaren superprocessesandlargescalenetworks
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Superprocesses and Large-Scale Networks

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