Related papers: Contour lines of the two-dimensional discrete Gaus…

Consider an instance $h$ of the Gaussian free field on a simply connected planar domain with boundary conditions $-\lambda$ on one boundary arc and $\lambda$ on the complementary arc, where $\lambda$ is the special constant $\sqrt{\pi/8}$.…

The level lines of the Gaussian free field are known to be related to SLE(4). It is shown how this relation allows to define chordal SLE(4) processes on doubly connected domains, describing traces that are anchored on one of the two…

We resolve a conjecture of Sheffield that $\SLE(4)$, a conformally invariant random curve, is the universal limit of the chordal zero-height contours of random surfaces with isotropic, uniformly convex potentials. Specifically, we study the…

Let $h$ be an instance of Gaussian Free Field in a planar domain. We study level lines of $h$ starting from boundary points. We show that the level lines are random continuous curves which are variants of SLE$_4$ path. We show that the…

The relation between level lines of Gaussian free fields (GFF) and SLE(4)-type curves was discovered by O. Schramm and S. Sheffield. A weak interpretation of this relation is the existence of a coupling of the GFF and a random curve, in…

We study the level lines of a Gaussian free field in a planar domain with general boundary data $F$. We show that the level lines exist as continuous curves under the assumption that $F$ is regulated (i.e., admits left and right limits at…

We point out a new simple way to couple the Gaussian Free Field (GFF) with free boundary conditions in a two-dimensional domain with the GFF with zero boundary conditions in the same domain: Starting from the latter, one just has to sample…

We apply some ideas of Bombieri and Garrett to construct natural self-adjoint operators on spaces of automorphic forms whose only possible discrete spectrum is $\lambda_{s}$ for $s$ in a subset of on-line zeros of an $L$-function, appearing…

We consider chordal SLE(kappa) curves for kappa > 4, where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension min {2-8/kappa,1}. We study the random sets of points at which the curve…

We derive a surprising correspondence between SLE$_{\kappa}(\rho)$ processes and light cones of the Gaussian free field (GFF). Recall that (one-sided, chordal, origin-seeded) SLE$_\kappa(\rho)$ processes are in some sense the simplest and…

We consider a coupling of the Gaussian free field with slit holomorphic stochastic flows, called ($\delta,\sigma$)-SLE, which contains known SLE processes (chordal, radial, and dipolar) as particular cases. In physical terms, we study a…

We develop a version of dipolar conformal field theory in a simply connected domain with the Dirichlet-Neumann boundary condition and central charge one. We prove that all correlation functions of the fields in the OPE family of Gaussian…

It was realized recently that the chordal, radial and dipolar SLEs are special cases of a general slit holomorphic stochastic flow. We characterize those slit holomorphic stochastic flows which generate level lines of the Gaussian free…

Let $\kappa\in(4,8)$. Let $\gamma$ be an SLE$_\kappa$ curve in a Jordan domain $D$ connecting $a_1\ne a_2\in\partial D$. We attach $\gamma$ with two open boundary arcs $A_1,A_2$ of $D$, which share end points $b_1\ne b_2\in\partial…

In this paper we study the properties of the centered (norm of the) gradient squared of the discrete Gaussian free field in $U_{\epsilon}=U/\epsilon\cap \mathbb{Z}^d$, $U\subset \mathbb{R}^d$ and $d\geq 2$. The covariance structure of the…

We study two-valued local sets, $\mathbb{A}_{-a,b}$, of the two-dimensional continuum Gaussian free field (GFF) with zero boundary condition in simply connected domains. Intuitively, $\mathbb{A}_{-a,b}$ is the (random) set of points…

We consider a higher derivative scalar field theory in the presence of a boundary and a classically marginal interaction. We first investigate the free limit where the scalar obeys the square of the Klein-Gordon equation. In precisely $d=6$…

We study the extremal process associated with the Discrete Gaussian Free Field on the square lattice and elucidate how the conformal symmetries manifest themselves in the scaling limit. Specifically, we prove that the joint process of…

The nature of level set percolation in the two-dimension Gaussian Free Field has been an elusive question. Using a loop-model mapping, we show that there is a nontrivial percolation transition, and characterize the critical point. In…

For $d \geq 3$ we obtain an approximation of the zero-average Gaussian free field on the discrete $d$-dimensional torus of large side length $N$ by the Gaussian free field on $\mathbb Z^d$, valid in boxes of roughly side length $N -…