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PhD Studentship: Long-term Behaviour of Markov Chains

The University of Manchester

Qualification Type: PhD
Location: Manchester
Funding for: UK Students, EU Students, International Students
Funding amount: £18,622
Hours: Full Time
Placed On: 13th November 2023
Closes: 14th January 2024

Several projects are available, studying idealised Markovian models of epidemic, population and network processes. The emphasis will mostly be on theoretical aspects of the models, involving advanced probability theory.

For instance, there are a number of stochastic models of epidemics where the course of the epidemic is known to follow the solution of a differential equation over short time intervals, but where little or nothing has been proved about the long-term behaviour of the stochastic process. Techniques have been developed for studying such problems, and a project might involve adapting these methods to new settings.

Depending on the preference of the candidate, a project might involve a substantial computational component, gaining insights into the behaviour of a model, via simulations, ahead of proving rigorous theoretical results.

The project is funded by the Leverhulme Trust, in association with the award of a Leverhulme International Professorship for Professor Luczak. The funding covers tuition fees and a tax free stipend set at the UKVI rate (£18,622 in 2023/24). We are able to offer a limited number of studentships to applicants outside the UK. Therefore, full studentships will only be awarded to exceptional quality candidates, due to the competitive nature of this scheme.

Applicants should have, or expect to achieve, a Merit in a taught master's degree (or equivalent) in a related discipline and a 2:1 degree or equivalent in mathematics.

Please contact Professor Luczak is malwina.luczak@mancester.ac.uk to apply.

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