Georgia Institute of Technology College of Sciences

Gaussian fields with logarithmically decaying correlations, such as branching Brownian motion and the 2D Gaussian free field, are conjectured to form a new universality class of extreme value statistics (notably in the work of Carpentier & Ledoussal and Fyodorov & Bouchaud). This class is the borderline case between the class of IID random variables, and models where correlations start to affect the statistics. In this talk, I will report on the recent rigorous progress in describing the new features of this class. In particular, I will describe the emergence of Poisson-Dirichlet statistics. This is joint work with Olivier Zindy.