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2009 Special points of the Brownian net
Emmanuel Schertzer, Rongfeng Sun, Jan Swart
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Electron. J. Probab. 14: 805-864 (2009). DOI: 10.1214/EJP.v14-641

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.

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Emmanuel Schertzer. Rongfeng Sun. Jan Swart. "Special points of the Brownian net." Electron. J. Probab. 14 805 - 864, 2009. https://doi.org/10.1214/EJP.v14-641

Information

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

zbMATH: 1187.82081
MathSciNet: MR2497454
Digital Object Identifier: 10.1214/EJP.v14-641

Subjects:
Primary: 82C21
Secondary: 60D05 , 60K35

Keywords: branching-coalescing point set , Brownian net , Brownian web

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