The Brownian web is a collection of one-dimensional coalescing Brownian motions starting from every point in space and time, while the Brownian net is an extension that also allows branching. The Brownian net is proved to be the universal scaling limit of one-dimensional branching-coalescing random walks with weak binary branching and arbitrary increment distributions that have sufficient moments and it is conjectured to be the limit in case of more general (non-binary) weak branching.
However, the present methodology of proving convergence appears to be very limited while dealing with a dependent set of paths with weak branching.
In this talk we will give a new characterization and provide alternate convergence conditions. We will show that these new conditions are more robust for studying convergence problems to the Borwnian net.
