Perturbations of Supercritical Oriented Percolation and Sticky Brownian Webs

Abstract

Previously, Sarkar and Sun [13] have shown that for supercritical oriented percolation in dimension 1 + 1, the set of rightmost infinite open paths converges to the Brownian web after proper centering and scaling. In this note, we show that a pair of sticky Brownian webs arise naturally if one considers the set of right-most infinite open paths for two coupled percolation configurations with distinct (but close) percolation parameters. This leads to a natural conjecture on the convergence of the dynamical supercritical oriented percolation model to the so-called dynamical Brownian web.