A note on oriented percolation with inhomogeneities and strict inequalities

TL;DR

This paper investigates how the percolation threshold behaves in oriented percolation models with layered inhomogeneities and long-range dependence, focusing on the effect of adding an extra dimension.

Contribution

It provides new insights into the strict decrease of the percolation parameter in layered, inhomogeneous environments with long-range dependence.

Findings

Percolation threshold decreases strictly when an extra dimension is added.

Analysis of inhomogeneous layered environments with long-range dependence.

Insights into the behavior of oriented percolation under complex conditions.

Abstract

This note was motivated by natural questions related to oriented percolation on a layered environment that introduces long range dependence. As a convenient tool, we are led to deal with questions on the strict decrease of the percolation parameter in the oriented setup when an extra dimension is added.