Abstract
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.
Citation
Rongfeng Sun. Jan M. Swart. "The Brownian net." Ann. Probab. 36 (3) 1153 - 1208, May 2008. https://doi.org/10.1214/07-AOP357
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