The Brownian web is a collection of coalescing one-dimensional Brownian motions, starting from each point in space and time. It arises as the diffusive scaling limit of a collection of coalescing random walks. In joint work with Jan M. Swart, we construct a generalization of the Brownian web by allowing branching, which we call the Brownian net.
In this talk, we introduce the Brownian net and explain some of its basic properties. Part of the material presented is also joint work with Jan Swart and Emmanuel Schertzer.