Related papers: Level Set Percolation in Two-Dimensional Gaussian …
For the Gaussian free field on a $(d + 1)$-regular tree with $d \geq 2$, we study the percolative properties of its level sets in the critical and the near-critical regime. In particular, we show the continuity of the percolation…
We study level-set percolation for Gaussian free fields on metric graphs. In two dimensions, we give an upper bound on the chemical distance between the two boundaries of a macroscopic annulus. Our bound holds with high probability…
We study the level-set percolation of the Gaussian free field on Z^d, d bigger or equal to 3. We consider a level alpha such that the excursion-set of the Gaussian free field above alpha percolates. We derive large deviation estimates on…
We investigate level-set percolation of the Gaussian free field on transient trees, for instance on super-critical Galton-Watson trees conditioned on non-extinction. Recently developed Dynkin-type isomorphism theorems provide a comparison…
In this paper we introduce the two-sided level-set for the two-dimensional discrete Gaussian free field. Then we investigate the chemical distance for the two-sided level-set percolation. Our result shows that the chemical distance should…
We study level-set percolation of the Gaussian free field on the infinite $d$-regular tree for fixed $d\geq 3$. Denoting by $h_\star$ the critical value, we obtain the following results: for $h>h_\star$ we derive estimates on conditional…
We consider the Gaussian free field on two-dimensional slabs with a thickness described by a height $h$ at spatial scale $N$. We investigate the radius of critical clusters for the associated cable-graph percolation problem, which depends…
We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…
We study percolation of two-sided level sets for the discrete Gaussian free field (DGFF) in 2D. For a DGFF $\varphi$ defined in a box $B_N$ with side length $N$, for $C$ large enough, there exist low crossings in the set of vertices $z$…
It is believed that the large-scale geometric properties of two-dimensional critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities…
We consider a general enough set-up and obtain a refinement of the coupling between the Gaussian free field and random interlacements recently constructed by Titus Lupu in arXiv:1402.0298. We apply our results to level-set percolation of…
We prove that the set of thick points of the log-correlated Gaussian field contains an unbounded path in sufficiently high dimensions. This contrasts with the two-dimensional case, where Aru, Papon, and Powell (2023) showed that the set of…
We consider continuous-time random interlacements on Z^d, d greater or equal to 3, and investigate the percolation model where a site x of Z^d is occupied if the total amount of time spent at x by all the trajectories of the interlacement…
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 as the mesh size $\delta$ goes to 0. In…
The two-dimensional site percolation problem is studied by transfer-matrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and critical indices, predicted by conformal…
We consider upper level-sets of the Gaussian free field on $\mathbb Z^d$, for $d\geq 3$, above a given real-valued height parameter $h$. As $h$ varies, this defines a canonical percolation model with strong, algebraically decaying…
We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the…
We consider the zero-average Gaussian free field on a certain class of finite $d$-regular graphs for fixed $d\geq 3$. This class includes $d$-regular expanders of large girth and typical realisations of random $d$-regular graphs. We show…
We consider level-set percolation for the Gaussian free field on Z^d, with d bigger or equal to 3, and prove that there is a non-trivial critical level h_* such that for h > h_*, the excursion set above level h does not percolate, and for h…
We study percolative properties of excursion processes and the discrete Gaussian free field (dGFF) in the planar unit disk. We consider discrete excursion clouds, defined using random walks as a two-dimensional version of random…