Two-temperatures overlap distribution for the 2D discrete Gaussian free field

Extreme values for two-dimensional discrete Gaussian free field

We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on the gap between the two largest maxima, and precise (in the exponential scale) estimate for the right tail on the law of the centered maximum.

Contour lines of the two-dimensional discrete Gaussian free field

We prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there is a constant λ > 0 such that when h is an interpolation of the discrete Gaussian free field on a Jordan domain — with boundary values −λ on one boundary arc and λ on the complementary arc — the zero level line of h joining the endpoints of these arcs converges to SLE(4) ...

Tightness of the Recentered Maximum of the Two–dimensional Discrete Gaussian Free Field

We consider the maximum of the discrete two dimensional Gaussian free field (GFF) in a box, and prove that its maximum, centered at its mean, is tight, settling a long–standing conjecture. The proof combines a recent observation of [BDZ10] with elements from [Br78] and comparison theorems for Gaussian fields. An essential part of the argument is the precise evaluation, up to an error of order 1...

BERLIN-LEIPZIG WORKSHOP MARCH 2013 TALKS AND ABSTRACTS Marek Biskup: Law of the extremes for the two dimensional discrete Gaussian Free Field Abstract: A two-dimensional discrete Gaussian Free Field

A two-dimensional discrete Gaussian Free Field (DGFF) is a Gaussian process indexed by the vertices in a finite set, e.g., a square, in the square lattice. The process is centered (mean zero) and the covariance is given by the Green function of the simple random walk killed upon exiting from the set. Recently, much effort has been paid to the study of the concentration properties and tail estim...

Topics on the two-dimensional Gaussian Free Field