### Description:

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:

**The maximum of log-correlated Gaussian fields in random environments**

Authors: Florian Schweiger, Ofer Zeitouni**Tightness for branching random walk in time-inhomogeneous random environment**

Author: Xaver Kriechbaum**On the limiting law of line ensembles of Brownian polymers with geometric area tilts**

Authors: Amir Dembo, Eyal Lubetzky, Ofer Zeitouni**Moments of partition functions of 2D Gaussian polymers in the weak disorder regime -- I**

Authors: Clement Cosco, Ofer Zeitouni**Asymptotics of the p-capacity in the critical regime**

Authors: Clement Cosco, Shuta Nakajima, Florian Schweiger**The extremal point process of branching Brownian motion in R^d**

Authors: Julien Berestycki, Yujin H. Kim, Eyal Lubetzky, Bastien Mallein, Ofer Zeitouni**Concentration of the complexity of spherical pure p-spin models at arbitrary energies**

Authors: Eliran Subag, Ofer Zeitouni**Universality of Poisson limits for moduli of roots of Kac polynomials**

Authors: Nicholas A. Cook, Hoi H. Nguyen, Oren Yakir, Ofer Zeitouni**The maximum of branching Brownian motion in R^d**

Authors: Yujin H. Kim, Eyal Lubetzky, Ofer Zeitouni**Universality in outliers for weakly confined Coulomb gases**

Authors: Raphael Butez, David Garcia-Zelada, Alon Nishry, Aron Wennman**A variational formula for large deviations in first-passage percolation under tail estimates**

Authors: Clement Cosco, Shuta Nakajima-
**Localization of eigenvectors of non-Hermitian banded noisy Toeplitz matrices**

Authors: Anirban Basak, Martin Vogel, Ofer Zeitouni -
**A CLT for the characteristic polynomial of random Jacobi matrices, and the GβE**

Authors: Fanny Augeri, Raphael Butez, Ofer Zeitouni -
**Directed polymers on infinite graphs**

Authors: Clement Cosco, Inbar Seroussi, Ofer Zeitouni **A Spectral Condition for Spectral Gap: Fast Mixing in High-Temperature Ising Models**

Authors**:**Ronen Eldan, Frederic Koehler, Ofer Zeitouni-
**The minimum modulus of Gaussian trigonometric polynomials**

Authors**:**Oren Yakir, Ofer Zeitouni -
**A local CLT for linear statistics of 2D Coulomb gases**

Authors**:**Thomas Leblé, Ofer Zeitouni -
**Laws of large numbers and fluctuations in the sub-critical and L^2 phases for the SHE and KPZ equation in dimension d>=3**

Authors: Clement Cosco, Shuta Nakajima, Makoto Nakashima -
**The Erdős-Rényi law of large numbers for ballistic random walk in random environment**

Authors**:**Darcy Camargo, Yuri Kifer, Ofer Zeitouni -
**Deterministic equivalence for noisy perturbations**

Authors**:**Martin Vogel, Ofer Zeitouni -
**Moderate deviations for the self normalized walk on random scenery**

Authors: Tal Peretz **Subsequential tightness for branching random walk in random environment**

Authors: Xaver Kriechbaum-
**Large deviations for the largest eigenvalue of subGaussian matrices**

Authors: Fanny Augeri, Alice Guionnet, Jonathan Husson -
**A transportation approach to the mean field approximation**

Authors: Fanny Augeri -
**Limit law for the cover time of a random walk on a binary tree**

Authors**:**Amir Dembo, Jay Rosen, Ofer Zeitouni -
**Outliers of random perturbations of Toeplitz matrices with finite symbols**

Authors**:**Anirban Basak, Ofer Zeitouni -
**Spectrum of random perturbations of Toeplitz matrices with finite symbols**

Authors**:**Anirban Basak, Elliot Paquette, Ofer Zeitouni -
**Fluctuations of the solutions to the KPZ equation in dimensions three and higher**

Authors**:**Alexander Dunlap, Yu Gu, Lenya Ryzhik, Ofer Zeitouni -
**Maximum of Branching Brownian motion in a periodic environment**

Authors**:**Eyal Lubetzky, Chris Thornett, Ofer Zeitouni -
**The random heat equation in dimensions three and higher: the homogenization viewpoint**

Authors**:**Alexander Dunlap, Yu Gu, Lenya Ryzhik, Ofer Zeitouni -
**Heat kernel for Liouville Brownian motion and Liouville graph distance**

Authors**:**Jian Ding, Ofer Zeitouni, Fuxi Zhang -
**Maximum of the characteristic polynomial for a random permutation matrix**

Authors: Nicholas Cook, Ofer Zeitouni -
**Geometry and temperature chaos in mixed spherical spin glasses at low temperature - the perturbative regime**

Authors**:**Gérard Ben Arous, Eliran Subag, Ofer Zeitouni -
**Subsequential tightness of the maximum of two dimensional Ginzburg-Landau fields**

Authors: Wei Wu, Ofer Zeitouni **Extremal particles of two dimensional Copulomb gases and random polynomials on a positive background**

Authors: Raphael Butez, David Garcia-Zelada**Tightness for the Cover Time of the two dimensional sphere**

Authors**:**David Belius, Jay Rosen, Ofer Zeitouni-
**The Edwards-Wilkinson limit of the random heat equation in dimensions three and higher**

Authors: Yu Gu, Lenya Ryzhik, Ofer Zeitouni -
**Barrier estimates for a critical Galton--Watson process and the cover time of the binary tree**

Authors: David Belius, Jay Rosen, Ofer Zeitouni -
**Nonlinear large deviations bounds with applications to Wigner matrices and sparse Erdos-Renyi graphs**

Authors: Fanny Augeri -
**The Curie-Weiss model with complex temperature: phase transitions**

Authors: Mira Shamis, Ofer Zeitouni -
**On the Liouville heat kernel for k-coarse MBRW and nonuniversality**

Authors: Jian Ding, Ofer Zeitouni, Fuxi Zhang -
**The law of large numbers for the maximum of almost Gaussian log-correlated fields coming from random matrices**

Authors: Gaultier Lambert, Elliot Paquette -
**The maximum of the CUE field**

Authors: Elliot Paquette, Ofer Zeitouni