Scaling limit of the radial Poissonian web

2014/03/20 by Luiz Renato Fontes, Fontes, Luiz Renato, León A. Valencia +4
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #Point processes and geometric inequalities #Stochastic processes and statistical mechanics #math.PR #msc:60K35

paper · pdf · doi:10.48550/arxiv.1403.5286

arxiv created 2014/03/20 · arxiv updated 2014/03/24

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.

Citations

• Convergence of Coalescing Nonsimple Random Walks to the Brownian Web
• Random directed forest and the Brownian web

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