The Brownian web: Characterization and convergence

Details The Brownian web: Characterization and convergence The Brownian web: Characterization and convergence

2003-11-15

arxiv.org/abs/math/0311254v2

Annals of Probability 2004, Vol. 32, No. 4, 2857-2883

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000568 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000568

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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