This project is mainly concerned with the study of atypical values of a class of spatial processes that are, loosely speaking, logarithmically correlated; the main example is the Gaussian free field (GFF). Renewed interest in the GFF derives from several strands that have seen revolutionary progress in the last decades, such as the appearance of Loewner-Schramm Evolution (SLE) in the level sets of the GFF, the rapid development (by Sheffield, Duplantier, Miller and others) of quantum gravity (which aims at modelling random surfaces) in terms of the (formal) exponential of the GFF, the appearance of GFF in the study of linear statistics of random matrices, the appearance of logarithmically correlated structures (not necessarily Gaussian) in the study of thick points and cover time for planar Brownian and in the study of determinants of random matrices, and their relation with the Riemann zeta function.

The study of the extremes of the GFF has seen rapid progress in recent years, culminating with the proof of convergence in distribution of the maximum and of a related extremal process. This progress was made possible by exploiting links with other logarithmically correlated processes, and in particular with branching random walks. A major objective of the project is to develop the general heuristics leading to convergence of extrema processes for logarithmically correlated fields, both Gaussian and non-Gaussian, into a universal theory, as well as develop various applications, especially to random matrices, branching processes in inhomogeneous environments, random polynomials, and spectral theory.

Team members (at different times):

Fanny Augeri, Anirban Basak, Raphael Butez, Darcy Camargo, Clement Cosco, Xaver Kriechbaum, Elliot Paquette, Tal Peretz, Florian Schweiger, Inbar Seroussi, Mira Shamis, Ofer Zeitouni.

Some project Images:







List of publications: