A new look at the interfaces in percolation
Résumé
We propose a new definition of the interface in the context of the Bernoulli percolation model. We construct a coupling between two percolation configurations , one which is a standard percolation configuration, and one which is a percolation configuration conditioned on a disconnection event. We define the interface as the random set of the edges where these two configurations differ. We prove that, inside a cubic box Λ, the interface between the top and the bottom of the box is typically localized within a distance of order (ln |Λ|)^2 of the set of the pivotal edges.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...