## 46 Citations

### Level lines of the Gaussian Free Field with general boundary data

- Mathematics
- 2015

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…

### Level Lines of Gaussian Free Field II: Whole-Plane GFF

- Mathematics
- 2015

We study the level lines of GFF starting from interior points. We show that the level line of GFF starting from an interior point turns out to be a sequence of level loops. The sequence of level…

### The First Passage Sets of the 2D Gaussian Free Field: Convergence and Isomorphisms

- Mathematics
- 2018

In a previous article, we introduced the first passage set (FPS) of constant level $$-a$$ - a of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it…

### First passage sets of the 2D continuum Gaussian free field

- MathematicsProbability Theory and Related Fields
- 2019

We introduce the first passage set (FPS) of constant level $$-a$$ - a of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set of points in…

### Coupling the Gaussian Free Fields with Free and with Zero Boundary Conditions via Common Level Lines

- Mathematics, PhysicsCommunications in Mathematical Physics
- 2018

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…

### Coupling the Gaussian Free Fields with Free and with Zero Boundary Conditions via Common Level Lines

- Mathematics, PhysicsCommunications in Mathematical Physics
- 2018

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…

### Crossing estimates from metric graph and discrete GFF

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2022

We compare level-set percolation for Gaussian free fields (GFFs) defined on a rectangular subset of $\delta \mathbb{Z}^2$ to level-set percolation for GFFs defined on the corresponding metric graph…

### Statistical reconstruction of the Gaussian free field and KT transition

- Mathematics
- 2020

In this paper, we focus on the following question. Assume $\phi$ is a discrete Gaussian free field (GFF) on $\Lambda \subset \frac 1 n \mathbb{Z}^2$ and that we are given $e^{iT \phi}$, or…

### Convergence of the Critical Planar Ising Interfaces to Hypergeometric SLE

- Mathematics
- 2016

We consider the planar Ising model in rectangle $(\Omega; x^L, x^R, y^R, y^L)$ with alternating boundary condition: $\ominus$ along $(x^Lx^R)$ and $(y^Ry^L)$, $\xi^R\in\{\oplus, \text{free}\}$ along…

### Exit sets of the continuum Gaussian free field in two dimensions and related questions

- Mathematics
- 2017

The topic of this thesis is the study of geometric properties of the two-dimensional continuum Gaussian free field (GFF), which is the analogue of Brownian motion when time is replaced by a…

## References

SHOWING 1-10 OF 38 REFERENCES

### Level lines of the Gaussian Free Field with general boundary data

- Mathematics
- 2015

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…

### Level Lines of Gaussian Free Field II: Whole-Plane GFF

- Mathematics
- 2015

We study the level lines of GFF starting from interior points. We show that the level line of GFF starting from an interior point turns out to be a sequence of level loops. The sequence of level…

### SLE and the free field: partition functions and couplings

- Mathematics
- 2007

Schramm-Loewner Evolutions ($\SLE$) are random curves in planar simply connected domains; the massless (Euclidean) free field in such a domain is a random distribution. Both have conformal invariance…

### A contour line of the continuum Gaussian free field

- Mathematics
- 2010

Consider an instance $$h$$ of the Gaussian free field on a simply connected planar domain $$D$$ with boundary conditions $$-\lambda $$ on one boundary arc and $$\lambda $$ on the complementary arc,…

### Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees

- Mathematics
- 2013

We establish existence and uniqueness for Gaussian free field flow lines started at interior points of a planar domain. We interpret these as rays of a random geometry with imaginary curvature and…

### Contour lines of the two-dimensional discrete Gaussian free field

- Mathematics
- 2006

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…

### Imaginary geometry I: interacting SLEs

- Mathematics
- 2012

Fix constants $$\chi >0$$χ>0 and $$\theta \in [0,2\pi )$$θ∈[0,2π), and let h be an instance of the Gaussian free field on a planar domain. We study flow lines of the vector field $$e^{i(h/\chi…

### Intersections of SLE Paths: the double and cut point dimension of SLE

- Mathematics
- 2013

We compute the almost-sure Hausdorff dimension of the double points of chordal $$\mathrm {SLE}_\kappa $$SLEκ for $$\kappa > 4$$κ>4, confirming a prediction of Duplantier–Saleur (1989) for the…

### Conformal invariance of planar loop-erased random walks and uniform spanning trees

- Mathematics
- 2001

This paper proves that the scaling limit of a loop-erased random walk in a simply connected domain \(D\mathop \subset \limits_ \ne \mathbb{C} \) is equal to the radial SLE2 path. In particular, the…

### Height Fluctuations in the Honeycomb Dimer Model

- Mathematics
- 2004

We study a model of random surfaces arising in the dimer model on the honeycomb lattice. For a fixed “wire frame” boundary condition, as the lattice spacing ϵ → 0, Cohn, Kenyon and Propp [3] showed…