Generalised oriented site percolation, probabilistic cellular automata and bootstrap percolation

Ivailo Hartarsky, Réka Szabó

Published 2021-03-29Version 1

Motivated by applications to probabilistic cellular automata (PCA) and bootstrap percolation (BP), we consider a generalised oriented site percolation model (GOSP) on $\mathbb{Z}^d$. We provide a broad user-oriented overview on the supercritical regime of this model with little to no proofs. Although not particularly novel for specialists on standard oriented percolation (OP), from the point of view of PCA and BP almost all results presented are new and some rectify previous works. Despite the resemblance with OP, some important difficulties arise for GOSP. Although we work with GOSP for simplicity, many of the techniques are much more general, so we hope that the survey will be of use in different settings.