CRITICAL BEHAVIOR FOR AN ORIENTED PERCOLATION WITH LONG-RANGE INTERACTIONS IN DIMENSION $d \gt 2$

Abstract

We consider a model of oriented percolation on ${\mathbb Z}^d \times {\mathbb Z}$, $d \gt 2$, with long-range interactions, in which the bond occupation probability decays as the $\alpha$-stable distribution with $\alpha = 1$. We use the lace expansion to get an $L^1$ infrared bound estimate which implies several critical exponents via the triangle condition.