Abstract
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×ℝ. We extend the earlier work of Arratia and of Tóth 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.
Citation
L. R. G. Fontes. M. Isopi. C. M. Newman. K. Ravishankar. "The Brownian web: Characterization and convergence." Ann. Probab. 32 (4) 2857 - 2883, October 2004. https://doi.org/10.1214/009117904000000568
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