The Annals of Probability

Journal: The Annals of Probability

Abbreviation

Ann. probab.

Publisher

Institute of Mathematical Statistics

ISSN

0091-1798
2168-894X

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Publications 1 - 10 of 44

An effective criterion and a new example for ballistic diffusions in random environment
Goergen, Laurent (2006)
The Annals of Probability
VISCOSITY SOLUTIONS OF FULLY NONLINEAR PARABOLIC PATH DEPENDENT PDES: PART II
Ekren, Ibrahim; Touzi, Nizar; Zhang, Jianfeng F. (2016)
The Annals of Probability
On the critical parameter of interlacement percolation in high dimension
Sznitman, Alain-Sol (2011)
The Annals of Probability
The phase transition for planar Gaussian percolation models without FKG
Muirhead, Stephen; Rivera, Alejandro; Vanneuville, Hugo; et al. (2023)
The Annals of Probability
We develop techniques to study the phase transition for planar Gaussian percolation models that are not (necessarily) positively correlated. These models lack the property of positive associations (also known as the 'FKG inequality'), and hence many classical arguments in percolation theory do not apply. More precisely, we consider a smooth stationary centred planar Gaussian field f and, given a level l epsilon R, we study the connectivity properties of the excursion set {f >= -l}. We prove the existence of a phase transition at the critical level l(crit) = 0 under only symmetry and (very mild) correlation decay assumptions, which are satisfied by the random plane wave for instance. As a consequence, all nonzero level lines are bounded almost surely, although our result does not settle the boundedness of zero level lines ('no percolation at criticality').To show our main result: (i) we prove a general sharp threshold criterion, inspired by works of Chatterjee, that states that 'sharp thresholds are equivalent to the delocalisation of the threshold location'; (ii) we prove threshold delocalisation for crossing events at large scales-at this step we obtain a sharp threshold result but without being able to locate the threshold-and (iii) to identify the threshold, we adapt Tassion's RSW theory replacing the FKG inequality by a sprinkling procedure. Although some arguments are specific to the Gaussian setting, many steps are very general and we hope that our techniques may be adapted to analyse other models without FKG.
Quenched exit estimates and ballisticity conditions for higher-dimensional random walk in random environment
Drewitz, Alexander; Ramírez, Alejandro F. (2012)
The Annals of Probability
Locality of percolation for Abelian Cayley graphs
Martineau, Sébastien; Tassion, Vincent (2017)
The Annals of Probability
Limit theorems for 2D invasion percolation
Damron, Michael; Sapozhnikov, Artëm (2012)
The Annals of Probability
A lower bound for disconnection by simple random walk
Li, Xinyi (2017)
The Annals of Probability
On macroscopic holes in some supercritical strongly dependent percolation models
Sznitman, Alain-Sol (2019)
The Annals of Probability
Random curves on surfaces induced from the Laplacian determinant
Kassel, Adrien; Kenyon, Richard (2017)
The Annals of Probability

Publications 1 - 10 of 44

Journal: The Annals of Probability

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