Electronic Journal of Probability

Special points of the Brownian net

Emmanuel Schertzer, Rongfeng Sun, and Jan Swart

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819491

Digital Object Identifier
doi:10.1214/EJP.v14-641

Mathematical Reviews number (MathSciNet)
MR2497454

Zentralblatt MATH identifier
1187.82081

Subjects
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]

Keywords
Brownian net Brownian web branching-coalescing point set

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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