Generalised oriented site percolation

TL;DR

This paper introduces a generalized oriented site percolation model on multidimensional lattices with arbitrary neighborhoods, demonstrating that it behaves similarly to standard oriented percolation in the supercritical phase despite asymmetries.

Contribution

It extends the understanding of oriented percolation models by analyzing a more general version with asymmetries and arbitrary neighborhoods, showing similar supercritical behavior.

Findings

GOSP behaves like OP in the supercritical regime

Asymmetries and lack of planarity do not alter supercritical behavior

The model broadens the applicability of percolation theory

Abstract

We consider a generalised oriented site percolation model (GOSP) on $\mathbb Z^d$ with arbitrary neighbourhood. The key additional difficulties as compared to standard oriented percolation (OP) are the lack of symmetry and, in two dimensions, of planarity. We establish that, despite these deficiencies, in the supercritical regime GOSP behaves qualitatively like OP.