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The Brownian net

Rongfeng Sun·Jan M. Swart
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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.

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Rongfeng Sun, Jan M. Swart. 2008-06-13. The Brownian net. https://doi.org/10.1214/07-aop357

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