Electronic Journal of Probability

Special points of the Brownian net

Emmanuel Schertzer, Rongfeng Sun, and Jan Swart

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The Brownian net, which has recently been introduced by Sun and Swart [16], and independently by Newman, Ravishankar and Schertzer [13], generalizes the Brownian web by allowing branching. In this paper, we study the structure of the Brownian net in more detail. In particular, we give an almost sure classification of each point in $\mathbb{R}^2$ according to the configuration of the Brownian net paths entering and leaving the point. Along the way, we establish various other structural properties of the Brownian net.

Article information

Electron. J. Probab., Volume 14 (2009), paper no. 30, 805-864.

Accepted: 19 April 2009
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

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] 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Brownian net Brownian web branching-coalescing point set

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Schertzer, Emmanuel; Sun, Rongfeng; Swart, Jan. Special points of the Brownian net. Electron. J. Probab. 14 (2009), paper no. 30, 805--864. doi:10.1214/EJP.v14-641. https://projecteuclid.org/euclid.ejp/1464819491

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