The Brownian net

Details The Brownian net The Brownian net

2006-10-20

arxiv.org/abs/math/0610625v5

Annals of Probability 2008, Vol. 36, No. 3, 1153-1208

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP357 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/07-AOP357

The (standard) Brownian web is a collection of coalescing one- dimensional Brownian motions, starting from each point in space and time. It arises as the diffusive scaling limit of a collection of coalescing random walks. We show that it is possible to obtain a nontrivial limiting object if the random walks in addition branch with a small probability. We call the limiting object the Brownian net, and study some of its elementary properties.

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