Two-dimensional Poisson Trees converge to the Brownian web

Details Two-dimensional Poisson Trees converge to the Brownian web Two-dimensional Poisson Trees converge to the Brownian web

2003-04-17

arxiv.org/abs/math/0304247v2

Ann. Inst. H. Poincar\~A\c{opyright} Probab. Statist. 41 (2005), no. 5, 851--858

Mathematics

Probability

22 pages, 1 figure. This version corrects an error in the previous proof. The results are the same

Scientific paper

10.1016/j.anihpb.2004.06.003

The Brownian web can be roughly described as a family of coalescing one-dimensional Brownian motions starting at all times in $\R$ and at all points of $\R$. It was introduced by Arratia; a variant was then studied by Toth and Werner; another variant was analyzed recently by Fontes, Isopi, Newman and Ravishankar. The two-dimensional \emph{Poisson tree} is a family of continuous time one-dimensional random walks with uniform jumps in a bounded interval. The walks start at the space-time points of a homogeneous Poisson process in $\R^2$ and are in fact constructed as a function of the point process. This tree was introduced by Ferrari, Landim and Thorisson. By verifying criteria derived by Fontes, Isopi, Newman and Ravishankar, we show that, when properly rescaled, and under the topology introduced by those authors, Poisson trees converge weakly to the Brownian web.

Affiliated with

Also associated with

No associations

Rating

Two-dimensional Poisson Trees converge to the Brownian web does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Two-dimensional Poisson Trees converge to the Brownian web, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two-dimensional Poisson Trees converge to the Brownian web will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-10549