Triangle Condition for Oriented Percolation in High Dimensions

Abstract

In this paper, we apply the Brydges-Spencer lace expansion and the Hara-Slade analysis to obtain the triangle condition for the nearest-neighbor oriented bond percolation in high dimensions and for the spread-out oriented bond percolation in $Z^d \times Z, d \geq 5$. Furthermore, we also establish the infrared bound in the subcritical region and the mean-field behavior for these models.