Scaling limit of the radial Poissonian web
Probability
2014-03-24 v1
Abstract
We consider a variant of the radial spanning tree introduced by Baccelli and Bordenave. Like the original model, our model is a tree rooted at the origin, built on the realization of a planar Poisson point process. Unlike it, the paths of our model have independent jumps. We show that locally our diffusively rescaled tree, seen as the collection of the paths connecting its sites to the root, converges in distribution to the Brownian Bridge Web, which is roughly speaking a collection of coalescing Brownian bridges starting from all the points of a planar strip perpendicular to the time axis, and ending at the origin.
Keywords
Cite
@article{arxiv.1403.5286,
title = {Scaling limit of the radial Poissonian web},
author = {Luiz Renato Fontes and Leon Valencia and Glauco Valle},
journal= {arXiv preprint arXiv:1403.5286},
year = {2014}
}