The Annals of Probability

The Brownian net

Rongfeng Sun and Jan M. Swart

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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.

Article information

Ann. Probab., Volume 36, Number 3 (2008), 1153-1208.

First available in Project Euclid: 9 April 2008

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Zentralblatt MATH identifier

Primary: 82C21: Dynamic continuum models (systems of particles, etc.)
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60F17: Functional limit theorems; invariance principles 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Brownian net Brownian web branching-coalescing random walks branching-coalescing point set


Sun, Rongfeng; Swart, Jan M. The Brownian net. Ann. Probab. 36 (2008), no. 3, 1153--1208. doi:10.1214/07-AOP357.

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