Long-term behaviour of Markov chains

About the project

About the Project 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. Eligibility Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline. Funding This 3.5 year Project is fully funded; tuition fees will be paid and you will receive an annual tax free allowance based on the UKRI rate (£20,780for 2025/26). We expect the stipend to increase each year. This project is open to home students and those with settled status. Before you apply We strongly recommend that you contact the supervisor for this project before you apply. Please include details of your current level of study, academic background and any relevant experience and include a paragraph about your motivation to study this PhD project. How to apply Apply online through our website: https://uom.link/pgr-apply-2425 When applying, you’ll need to specify the full name of this project, the name of your supervisor, if you already having funding or if you wish to be considered for available funding through the university, details of your previous study, and names and contact details of two referees. Your application will not be processed without all of the required documents submitted at the time of application, and we cannot accept responsibility for late or missed deadlines. Incomplete applications will not be considered. After you have applied you will be asked to upload the following supporting documents: Final Transcript and certificates of all awarded university level qualifications Interim Transcript of any university level qualifications in progress CV Supporting statement: A one or two page statement outlining your motivation to pursue postgraduate research and why you want to undertake postgraduate research at Manchester, any relevant research or work experience, the key findings of your previous research experience, and techniques and skills you’ve developed. (This is mandatory for all applicants and the application will be put on hold without it). Contact details for two referees (please make sure that the contact email you provide is an official university/work email address as we may need to verify the reference) English Language certificate (if applicable) If you have any questions about making an application, please contact our admissions team by emailing FSE.doctoralacademy.admissions@manchester.ac.uk . Equality, diversity and inclusion is fundamental to the success of The University of Manchester, and is at the heart of all of our activities. We know that diversity strengthens our research community, leading to enhanced research creativity, productivity and quality, and societal and economic impact. We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status. We also support applications from those returning from a career break or other roles. We consider offering flexible study arrangements (including part-time: 50%, 60% or 80%, depending on the project/funder). featuredproject16jan25 | featuredproject7sep25

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