Spectral properties of random matrices

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing in September 2019 for students seeking funding, or at any point in the academic year for self-funded students. The deadline for funded applications is the 10th May2019.

This project will be supervised by Dr Anna Maltsev on a topic aligned with Dr. Maltsev’s research interests, such as random matrix theory.

Random matrix theory is a very active field of mathematics at the intersection of analysis, probability, mathematical physics and mathematical finance with a lot of known and potential applications.

In this field we seek to prove theorems which are similar to the central limit theorem. The central limit theorem states that the sample mean tends to a gaussian distribution as the sample size grows, irrespective of the original distribution of the variables.
Analogously, in random matrix theory, one might start with a matrix whose entries are independent and identically distributed (called a Wigner matrix) and then examine various spectral properties of the matrix when the dimension of the matrix is large. Particularly, a major goal is to show that many of these properties do not depend on the exact probability distribution of the entries.

The specific questions to be pursued in this project will depend on the interests of the student and will be decided in consultation with the supervisor. Dr. Maltsev has diverse research interests, including random matrix theory, analysis on metric graphs and mathematical biology. Please contact Dr Anna Maltsev at [Email Address Removed] for further inquiries. This project is eligible for full funding, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. The application procedure is described on the School website.