The Number of Open Paths in Oriented Percolation

Olivier Garet (1) , Régine Marchand (1) , Jean-Baptiste Gouéré (2)

1 Probabilités et statistiques
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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 the introduction of adapted sequences of regenerating times and on subadditive arguments.

Mots clés: subadditive ergodic theorem; oriented percolation

Domaines: Probabilités [math.PR]

Olivier Garet, Régine Marchand, Jean-Baptiste Gouéré. The Number of Open Paths in Oriented Percolation. 2013. ⟨hal-00916083v2⟩