Log-correlated fields in random matrices & statistical physics

The study of complex systems is an active research topic with applications ranging from material science and machine learning to biology and Earth’s climate.

The purpose of this proposal is to develop a comprehensive mathematical understanding of a class of complex systems or stochastic processes called logarithmically-correlated fields.

The planned research aims to describe the fractal geometry of these random fields and rigorously show that they exhibit universal features.

The specific models of interest come from the theory of random matrices while the main motivations come from statistical physics.

The project leader intends to tackle these problems using recent analytic and probabilistic methods combining random matrix theory and random geometry. These research fields are topical, very competitive and underwent significant developments in the last decade. This proposal combines six concrete research problems.

Four of them are cutting-edge projects which are expected to have a strong impact in the probability theory and mathematical physics community while the others are more accessible and suitable for a PhD student supported by this grant.

Several international experts will also be involved in the project which will contribute to the scientific excellence at KTH and in Sweden.