An update on lower bounds for the critical values of oriented percolation models

TL;DR

This paper establishes new lower bounds for the critical points in oriented percolation models using stochastic domination by multitype Galton-Watson trees, applicable across various lattices and dimensions.

Contribution

It introduces a novel method of bounding critical points through stochastic domination, extending to diverse lattice structures and higher dimensions.

Findings

New lower bounds for critical points in oriented percolation models

Method applicable to multiple lattice types and dimensions

Enhanced understanding of percolation thresholds

Abstract

We obtain new lower bounds on the critical points for various models of oriented percolation. The method is to provide a stochastic domination of the percolation processes by multitype Galton-Watson trees. This can be apply to the classical bond and site oriented percolation on Z^2 , but also on other lattices such as inhomogeneous ones, and on dimension three.