The Number of Open Paths in Oriented Percolation
Résumé
We study the number $N_n$ of open paths of length $n$ in supercritical oriented percolation. We prove that on the percolation event $\{\inf N_n>0\}$, $N_n^{1/n}$ almost surely converges to a deterministic constant. The proof relies on subadditive arguments and on a recent result of Birkner, Cerny, Depperschmidt and Gantert about the behaviour of the random walk on the backbone of the infinite cluster of oriented percolation.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)