Special points of the Brownian net

Abstract

The Brownian net, which has recently been introduced by Sun and Swart [SS08], and independently by Newman, Ravishankar and Schertzer [NRS08], 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 $R^2$ 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.

In this revision the main improvements are in the presentation. Parts of the introduction have been rewritten and extended and some figures have been added. We also added an overview of global notation. 55 pages, 7 figures

References in corpus (3)

• The Brownian web: Characterization and convergence
• The Dynamical Discrete Web
• Marking (1,2) Points of the Brownian Web and Applications