00 2 The Brownian Web

Arratia, and later Tóth and Werner, constructed random processes that formally correspond to coalescing one-dimensional Brownian motions starting from every space-time point. We extend their work by constructing and characterizing what we call the Brown-ian Web as a random variable taking values in an appropriate (metric) space whose points are (compact) sets of paths. This leads to general convergence criteria and, in particular , to convergence in distribution of coalescing random walks in the scaling limit to the Brownian Web.