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Special points of the Brownian net
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Emmanuel Schertzer, Columbia University
Rongfeng Sun, National University of Singapore
Jan M. Swart, Institute of Information Theory and Automation of the ASCR (UTIA)
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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 R2 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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Full text: PDF
Pages: 805-864
Published on: April 19, 2009
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