PhD Studentship: Spectral Correlations of Random Matrices

Loughborough University

Application details:

Start date of studentship: 1st October 2018

Closing date for applications: 16th February 2018

Supervisors:

Primary supervisor: Dr Brian Winn

Secondary supervisor: Dr Wael Bahsoun

Random matrices were introduced in the early part of the 20th Century to model the statistical behaviour of nuclear resonances in Physics, with immediate success, shedding light on hitherto unexplained behaviour.  Since then interest in the subject has exploded, particularly over the last 20 years, with applications in areas as diverse as number theory, statistical physics, quantum chaos, algebraic geometry and financial mathematics.

This project offers an opportunity to contribute to the state-of-the-art of knowledge about these fascinating objects.

Loughborough University is a top-ten rated university in England for research intensity (REF2014). In choosing Loughborough for your research, you’ll work alongside academics who are leaders in their field. You will benefit from comprehensive support and guidance from our Doctoral College, including tailored careers advice, to help you succeed in your research and future career.

See: www.lboro.ac.uk/study/postgraduate/supporting-you/research

Full Project Detail:

A random matrix is a matrix whose entries are random variables. One of the goals in the subject is to extract information about the statistical distribution of the eigenvalues, and eigenvectors, from the underlying probability distribution of the matrix entries.  Often this can only be done in the limit of large matrix size, but where it can be done the mathematical results are intricate and beautiful.

Random matrices provide one way to model the risk associated with financial portfolio positions. This is usually regarded as the variance of the portfolio return, and can be calculated as a non-linear function of the covariance matrix. Principal Component Analysis allows to extract information about the covariance matrices from knowledge of the leading eigenvalues and their eigenvectors. For a portfolio associated to an eigenvector of the covariance matrix, the risk associated is simply the eigenvalue. Modelling the returns on a class of assets as random variables, the covariance matrix becomes a (symmetric) random matrix, allowing the power of that subject to be brought to bear on the problem. However, many questions remain unanswered, including the important question of the most appropriate probability distribution to model financial returns.

The successful candidate will work with Drs Brian Winn/Wael Bahsoun to solve some key problems in this area and generate new knowledge.

Find out more:

www.lboro.ac.uk/departments/maths

www.lboro.ac.uk/science/study/postgraduate-research/studentships

Entry requirements:

Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Mathematics or a related subject. A relevant Master’s degree will be an advantage.

Funding information:

This studentship will be awarded on a competitive basis to applicants who have applied to this project and/or any of the advertised projects prioritised for funding by the School of Science.

The 3-year studentship provides a tax-free stipend of £14,553 (2017 rate) per annum (in line with the standard research council rates) for the duration of the studentship plus tuition fees at the UK/EU rate. International (non-EU) students may apply however the total value of the studentship will be used towards the cost of the International tuition fee in the first instance.

Contact details:

Name: Brian Winn

Email: b.winn@lboro.ac.uk

Tel: 01509-228220

How to apply:

Applications should be made online at www.lboro.ac.uk/study/apply/research. Under programme name, select Mathematical Sciences.

Please quote reference: BW/MA/2018

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Type / Role:

PhD

Location(s):

Midlands of England