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.
@article{schertzer_special_2009,
Author = {Schertzer, Emmanuel and Sun, Rongfeng and Swart, Jan
M.},
Title = {Special points of the {Brownian} net},
Journal = {Electronic Journal of Probability},
Volume = {14},
Number = {0},
Pages = {805--864},
Note = {Saisissez le texte ici},
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. },
doi = {10.1214/EJP.v14-641},
issn = {1083-6489},
month = apr,
url = {http://www.ams.org/books/memo/1065/},
urldate = {2015-02-18},
year = 2009
}
