Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree

Details Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree

2007-10-02

arxiv.org/abs/0710.0460v1

Mathematics

Probability

Scientific paper

In this article it is shown that the Brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete $n$-vertex ordered graph trees whose search-depth functions converge to the Brownian excursion as $n\to\infty$. We prove both a quenched version (for typical realisations of the trees) and an annealed version (averaged over all realisations of the trees) of our main result. The assumptions of the article cover the important example of simple random walks on the trees generated by the Galton-Watson branching process, conditioned on the total population size.

Affiliated with

Also associated with

No associations

Rating

Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree 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 Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-6989