Electronic Journal of Probability
- Electron. J. Probab.
- Volume 20 (2015), paper no. 31, 40 pp.
Scaling limit of the radial Poissonian web
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.
Electron. J. Probab., Volume 20 (2015), paper no. 31, 40 pp.
Accepted: 28 March 2015
First available in Project Euclid: 4 June 2016
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Valle, Glauco; Fontes, Luiz Renato; Valencia, Leon. Scaling limit of the radial Poissonian web. Electron. J. Probab. 20 (2015), paper no. 31, 40 pp. doi:10.1214/EJP.v20-3395. https://projecteuclid.org/euclid.ejp/1465067137