The Brownian net
Probability
2009-09-29 v5
Abstract
The (standard) Brownian web is a collection of coalescing one- dimensional Brownian motions, starting from each point in space and time. It arises as the diffusive scaling limit of a collection of coalescing random walks. We show that it is possible to obtain a nontrivial limiting object if the random walks in addition branch with a small probability. We call the limiting object the Brownian net, and study some of its elementary properties.
Cite
@article{arxiv.math/0610625,
title = {The Brownian net},
author = {Rongfeng Sun and Jan M. Swart},
journal= {arXiv preprint arXiv:math/0610625},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/07-AOP357 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)