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Special points of the Brownian net. (English) Zbl 1187.82081

Summary: The Brownian net, which has recently been introduced by R. Sun and J. M. Swart [Ann. Probab. 36, No. 3, 1153–1208 (2008; Zbl 1143.82020)], and independently by C. M. Newman, K. Ravishankar and E. Schertzer [Marking \((1,2)\) points of the Brownian web and applications, Math. Rev., arXiv:0806.0158 (2008)], 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.

MSC:

82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory

Citations:

Zbl 1143.82020
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