One PhD Studentships in Ergodic Theory and connections with Stochasticity
For students with a background, or interest in, one or more of
ergodic theory, probability theory, or stochastic analysis.
There are a number of subtopics related to the two main areas below that can be tailored to these interests.
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1. Deterministic systems (chaotic maps or ODEs) with more than one time scale can lead to limiting systems that are stochastic differential equations.
These can be driven by Brownian motion or by a Lévy process.
See
this paper
and
and this one.
The techniques involve generalising probabilistic ideas such as the central limit theorem and large deviations to the case of dynamical systems.
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2. Diffusion and anomalous diffusion in spatially-extended systems.
(From an ergodic theory point of view, spatially-extended = compact group extension with a restricted class of observables.)
A significant part of my work over last 10 years or so has been proving convergence to Brownian motion in such systems.
Recently this has included anomalous diffusion.
This preprint
is the state of the art regarding weak convergence to Brownian motion for such systems.
The studentship will pay a stipend for 4 years (subject to candidate
making good progress and meeting some standard requirements). It also
provides funding for travel to conferences.
How to Apply
You have to apply via the central university system (http://www2.warwick.ac.uk/study/postgraduate/apply/). Keep the following in mind:
Do not forget to mention my name as a possible PhD supervisor at Warwick (so that your application reaches me).
If you wish to start earlier than 1 October 2014, there will be a field in the on-line form that allows you do state this.
Although there is no deadline, it is advised to submit your application as soon as possible so that it receives full consideration.
Enquiries
I will be happy to answer informal enquiries (those that cannot be answered by the Postgraduate Admissions Team).
Thank you!
Ian Melbourne