Add to ORKGPreliminary draft We investigate the phase transition in a non-planar correlated percolation model with long-range dependence, obtained by considering level sets of a Gaussian free field with mass above a given height h. The dependence present in the model is a notorious impediment when trying to analyze the behavior near criticality. Alongside the critical threshold h ∗ for percolation, a second parameter h∗ ∗ ≥ h ∗ characterizes a strongly subcritical regime. We prove that the relevant crossing probabilities converge to 1 polynomially fast below h∗∗, which (firmly) sug-gests that the phase transition is sharp. A key tool is the derivation of a suitable differential inequality for the free field that enables the use of a (conditional) inf...
In this thesis we study various problems in dependent percolation theory. In the first part of this ...
We prove upper bounds on the one-arm exponent η1 for dependent percolation models; while our main in...
We consider a large class of inhomogeneous spatial random graphs on the real line. Each vertex carri...
38 pages, 4 figuresWe prove that the connectivity of the level sets of a wide class of smooth centre...
38 pages, 4 figuresWe prove that the connectivity of the level sets of a wide class of smooth centre...
38 pages, 4 figuresWe prove that the connectivity of the level sets of a wide class of smooth centre...
We develop techniques to study the phase transition for planar Gaussian percolation models that are ...
We prove that the connectivity of the level sets of a wide class of smooth centred planar Gaussian f...
40 pages, 14 figures, minor changes introduced and correction to proof of Lemma B.2. A paper by Step...
We consider self-avoiding walk and percolation in d, oriented percolation in d×+, and the contact pr...
We consider self-avoiding walk and percolation in d, oriented percolation in d×+, and the contact pr...
We consider the Gaussian free field on Zd, d≥3, and prove that the critical density for percolation ...
This thesis investigates the phase-transition phenomenon in a certain percolation model with long-ra...
Version accepted for publication. 36 pages, 3 figuresWe prove that the connectivity of the level set...
We consider the Gaussian free field on Zd, d ≥ 3, and prove that the critical density for percolatio...
In this thesis we study various problems in dependent percolation theory. In the first part of this ...
We prove upper bounds on the one-arm exponent η1 for dependent percolation models; while our main in...
We consider a large class of inhomogeneous spatial random graphs on the real line. Each vertex carri...
38 pages, 4 figuresWe prove that the connectivity of the level sets of a wide class of smooth centre...
38 pages, 4 figuresWe prove that the connectivity of the level sets of a wide class of smooth centre...
38 pages, 4 figuresWe prove that the connectivity of the level sets of a wide class of smooth centre...
We develop techniques to study the phase transition for planar Gaussian percolation models that are ...
We prove that the connectivity of the level sets of a wide class of smooth centred planar Gaussian f...
40 pages, 14 figures, minor changes introduced and correction to proof of Lemma B.2. A paper by Step...
We consider self-avoiding walk and percolation in d, oriented percolation in d×+, and the contact pr...
We consider self-avoiding walk and percolation in d, oriented percolation in d×+, and the contact pr...
We consider the Gaussian free field on Zd, d≥3, and prove that the critical density for percolation ...
This thesis investigates the phase-transition phenomenon in a certain percolation model with long-ra...
Version accepted for publication. 36 pages, 3 figuresWe prove that the connectivity of the level set...
We consider the Gaussian free field on Zd, d ≥ 3, and prove that the critical density for percolatio...
In this thesis we study various problems in dependent percolation theory. In the first part of this ...
We prove upper bounds on the one-arm exponent η1 for dependent percolation models; while our main in...
We consider a large class of inhomogeneous spatial random graphs on the real line. Each vertex carri...