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We consider the backbone of the infinite cluster generated by supercriticaloriented site percolation in dimension 1 +1. A directed random walk on thisbackbone can be seen as an "ancestral line" of an individual sampled in thestationary discrete-time contact process. Such ancestral lineages wereinvestigated in [BCDG13] where a central limit theorem for a single walker wasproved. Here, we consider infinitely many coalescing walkers on the samebackbone starting at each space-time point. We show that, after diffusiverescaling, the collection of paths converges in distribution to the Brownianweb. Hence, we prove convergence to the Brownian web for a particular system ofcoalescing random walks in a dynamical random environment. An important tool inthe proof is a tail bound on the meeting time of two walkers on the backbone,started at the same time. Our result can be interpreted as an averagingstatement about the percolation cluster: apart from a change of variance, itbehaves as the full lattice, i.e. the effect of the "holes" in the clustervanishes on a large scale.

Coalescing directed random walks on the backbone of a 1 +1-dimensional oriented percolation cluster converge to the Brownian web