  Previously, Sarkar and Sun 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.
