The Brownian web: Characterization and convergence

L. R. G. Fontes, M. Isopi, C. M. Newman, K. Ravishankar

Published 2003-11-15, updated 2005-04-06Version 2

The Brownian web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in R\timesR. We extend the earlier work of Arratia and of Toth and Werner by providing a new characterization which is then used to obtain convergence results for the BW distribution, including convergence of the system of all coalescing random walks to the BW under diffusive space-time scaling.