Associate Professor Oleg Zaboronski has been awarded a Leverhulme Research Fellowship for 2014–15 to investigate Eigenvalue processes for matrix-valued Brownian motions.

Exactly solvable agent-based (particle) models are of great interest in physics, biology and economics. For many such models, the statistical behaviour is universal and described by large random matrices. There is evidence that a fundamental particle system (Brownian particles killing each other or coagulating on contact) is also related to random matrices (populated with independent Brownian motions). The aim of the proposed research is to pin this relation down and generalize to more elaborate particle systems. Reaching this aim requires solution to a long-standing problem of dynamic correlations in random matrix theory thus advancing our understanding of stochastic processes associated with random matrices.