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The Brownian web: Characterization and convergence

L. R. G. Fontes·M. Isopi·C. M. Newman·K. Ravishankar
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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\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.

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L. R. G. Fontes, M. Isopi, C. M. Newman, K. Ravishankar. 2005-04-06. The Brownian web: Characterization and convergence. https://doi.org/10.1214/009117904000000568

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