The Brownian net

Rongfeng Sun; Jan M. Swart

doi:10.1214/07-AOP357

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Home > Journals > Ann. Probab. > Volume 36 > Issue 3 > Article

May 2008 The Brownian net

Rongfeng Sun, Jan M. Swart

Ann. Probab. 36(3): 1153-1208 (May 2008). DOI: 10.1214/07-AOP357

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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.