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Dr Cécile Mailler
No more applications being accepted
Competition Funded PhD Project (European/UK Students Only)
About the Project
This project is a discrete probability project on reinforced processes. These processes have a wide range of applications to, e.g., networks, genetics, and biology; a famous example is the preferential attachment random graph, which is used as a good model for large, complex, real-life networks such as the internet or social networks.
The project will focus on Pólya urns, which are the building blocks of all reinforced processes. A Pólya urn is a Markov chain describing the contents of an urn that contains balls of different colours. The original Pólya urns evolves as follows: at every (discrete) time-step, we draw a ball from the urn uniformly at random, and replace it in the urn together with an additional ball of the same colour. Many generalisations have been studied, in particular different “replacement rules”, and the goal is to prove asymptotic theorems (law of large numbers, central limit theorem) for the content of the urn at large time.
Although Pólya urns are classical objects in probability theory and have been studied for a hundred years, new recent developments have raised numerous open problems with exciting potential applications. For example, Pólya urns with infinitely-many colours were introduced in 2017 by the supervisor and collaborators; as well as being interesting from a purely theoretical point of view, proving asymptotic theorems about these urns gives a route to obtain exciting information about other stochastic objects such as random trees.
The project will be based in the internationally-recognised centre of probability at Bath, which is home to 9 staff members, 8 postdoc researchers, and 22 PhD students. The student will both benefit from and contribute to this dynamic research environment. Interested candidates are encouraged to direct informal enquires to Dr Cécile Mailler ([Email Address Removed]).
Formal applications should be made via the University of Bath’s online application form for a PhD in Mathematics (full-time):
https://www.bath.ac.uk/samis/urd/sits.urd/run/siw_ipp_lgn.login?process=siw_ipp_app&code1=RDUMA-FP03&code2=0012
More information about applying for a PhD at Bath may be found here:
http://www.bath.ac.uk/guides/how-to-apply-for-doctoral-study/
Anticipated start date: 1 October 2018
The project will focus on Pólya urns, which are the building blocks of all reinforced processes. A Pólya urn is a Markov chain describing the contents of an urn that contains balls of different colours. The original Pólya urns evolves as follows: at every (discrete) time-step, we draw a ball from the urn uniformly at random, and replace it in the urn together with an additional ball of the same colour. Many generalisations have been studied, in particular different “replacement rules”, and the goal is to prove asymptotic theorems (law of large numbers, central limit theorem) for the content of the urn at large time.
Although Pólya urns are classical objects in probability theory and have been studied for a hundred years, new recent developments have raised numerous open problems with exciting potential applications. For example, Pólya urns with infinitely-many colours were introduced in 2017 by the supervisor and collaborators; as well as being interesting from a purely theoretical point of view, proving asymptotic theorems about these urns gives a route to obtain exciting information about other stochastic objects such as random trees.
The project will be based in the internationally-recognised centre of probability at Bath, which is home to 9 staff members, 8 postdoc researchers, and 22 PhD students. The student will both benefit from and contribute to this dynamic research environment. Interested candidates are encouraged to direct informal enquires to Dr Cécile Mailler ([Email Address Removed]).
Formal applications should be made via the University of Bath’s online application form for a PhD in Mathematics (full-time):
https://www.bath.ac.uk/samis/urd/sits.urd/run/siw_ipp_lgn.login?process=siw_ipp_app&code1=RDUMA-FP03&code2=0012
More information about applying for a PhD at Bath may be found here:
http://www.bath.ac.uk/guides/how-to-apply-for-doctoral-study/
Anticipated start date: 1 October 2018
Funding Notes
UK and EU students applying for this project may be considered for a University Research Studentship which will cover Home/EU tuition fees, a training support fee of £1,000 per annum and a tax-free maintenance allowance at the RCUK Doctoral Stipend rate (£14,553 in 2017-18) for a period of 3.5 years.
Note: ONLY UK and EU applicants are eligible for this studentship; unfortunately, applicants who are classed as Overseas for fee paying purposes are NOT eligible for funding.
Note: ONLY UK and EU applicants are eligible for this studentship; unfortunately, applicants who are classed as Overseas for fee paying purposes are NOT eligible for funding.
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