  The Brownian web is a random object that occurs as the scaling limit of an
infinite system of coalescing random walks. Perturbing this system of random
walks by, independently at each point in space-time, resampling the random walk
increments, leads to some natural dynamics. In this paper we consider the
corresponding dynamics for the Brownian web. In particular, pairs of coupled
Brownian webs are studied, where the second web is obtained from the first by
perturbing according to these dynamics. A stochastic flow of kernels, which we
call the erosion flow, is obtained via a filtering construction from such
coupled Brownian webs, and the N-point motions of this flow of kernels are
identified.
