Brownian web in the scaling limit of supercritical oriented percolation in dimension 1 + 1

Abstract

We prove that, after centering and diffusively rescaling space and time, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice $Z^2_{\mathrm{even}}:=\{(x,i) in Z^2: x+i \mathrm{is even}\}$ converges in distribution to the Brownian web. This proves a conjecture of Wu and Zhang. Our key observation is that each rightmost infinite open path can be approximated by a percolation exploration cluster, and different exploration clusters evolve independently before they intersect.