Journal Articles Electronic Communications in Probability Year : 2021

Percolation and first-passage percolation on oriented graphs

Olivier Garet
Régine Marchand

Abstract

We give the first properties of independent Bernoulli percolation, for oriented graphs on the set of vertices $\Z^d$ that are translation-invariant and may contain loops. We exhibit some examples showing that the critical probability for the existence of an infinite cluster may be direction-dependent. Then, we prove that the phase transition in a given direction is sharp, and study the links between percolation and first-passage percolation on these oriented graphs.
Fichier principal
Vignette du fichier
percoo-fpp-eng-revision_21_05_25.pdf (220) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01837212 , version 1 (12-07-2018)
hal-01837212 , version 2 (03-06-2021)

Identifiers

Cite

Olivier Garet, Régine Marchand. Percolation and first-passage percolation on oriented graphs. Electronic Communications in Probability, 2021, 26, paper 50. ⟨10.1214/21-ECP419⟩. ⟨hal-01837212v2⟩
322 View
115 Download

Altmetric

Share

More