PhD opportunity in Bath
Wed 6 Mar 2013  10:36
PhD opportunity in Bath: "Statistics of paths in dynamic random networks"
Random networks (or random graphs) are idealised mathematical objects
which describe anything from social interactions to the chemical
reactions taking place inside a cell. Due to this wide applicability,
the mathematical theory of random networks has become an important and
very active area of research. The challenge of the field is to
investigate the structural properties of random graphs and prove
useful statements about their behaviour. For example, how do the rules
of the random graph affect the size of the connected components?
Historically, the most commonly studied random graph models are
static, in the sense that the graph is generated at random but then
remains fixed for all time. Of course, networks in the real world are
not like this: they change with time, growing (or possibly shrinking)
and adapting their structure. The mathematical theory of dynamic
random networks is far from complete, and even some basic properties
are not known. The aim of this project will be to investigate the
structural properties such random graphs, in particular in relation to
the statistics of paths between vertices. The mathematical methods
employed will draw on the theory of stochastic processes, branching
processes and graph theory.
You will be joining the probability group at the University of Bath; a
large and very active collection of academics, students and
researchers. Moreover, as part of the newlyformed Centre for Networks
and Collective Behaviour, you will also have the opportunity to
explore a diverse range of applications of the mathematical techniques
you will develop.
About the supervisors:
Tim Rogers holds a Prize Fellowship in mathematics. His research
interests include the structure and dynamics of networks, collective
effects in ecology and evolution, and random matrix theory.
Peter Mörters is a Professor of Probability, he is an expert in random
graphs and stochastic processes.

Peter Mörters
Professor of Probability and Head of Statistics Group
Department of Mathematical Sciences
University of Bath
Bath BA2 7AY
email: maspm@bath.ac.uk
tel: +44 (0)1225 386216
http://people.bath.ac.uk/maspm
Random networks (or random graphs) are idealised mathematical objects
which describe anything from social interactions to the chemical
reactions taking place inside a cell. Due to this wide applicability,
the mathematical theory of random networks has become an important and
very active area of research. The challenge of the field is to
investigate the structural properties of random graphs and prove
useful statements about their behaviour. For example, how do the rules
of the random graph affect the size of the connected components?
Historically, the most commonly studied random graph models are
static, in the sense that the graph is generated at random but then
remains fixed for all time. Of course, networks in the real world are
not like this: they change with time, growing (or possibly shrinking)
and adapting their structure. The mathematical theory of dynamic
random networks is far from complete, and even some basic properties
are not known. The aim of this project will be to investigate the
structural properties such random graphs, in particular in relation to
the statistics of paths between vertices. The mathematical methods
employed will draw on the theory of stochastic processes, branching
processes and graph theory.
You will be joining the probability group at the University of Bath; a
large and very active collection of academics, students and
researchers. Moreover, as part of the newlyformed Centre for Networks
and Collective Behaviour, you will also have the opportunity to
explore a diverse range of applications of the mathematical techniques
you will develop.
About the supervisors:
Tim Rogers holds a Prize Fellowship in mathematics. His research
interests include the structure and dynamics of networks, collective
effects in ecology and evolution, and random matrix theory.
Peter Mörters is a Professor of Probability, he is an expert in random
graphs and stochastic processes.

Peter Mörters
Professor of Probability and Head of Statistics Group
Department of Mathematical Sciences
University of Bath
Bath BA2 7AY
email: maspm@bath.ac.uk
tel: +44 (0)1225 386216
http://people.bath.ac.uk/maspm
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