Electronic Journal of Probability

Scaling limit of the radial Poissonian web

Glauco Valle, Luiz Renato Fontes, and Leon Valencia

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 31, 40 pp.

Dates
Accepted: 28 March 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067137

Digital Object Identifier
doi:10.1214/EJP.v20-3395

Mathematical Reviews number (MathSciNet)
MR3335822

Zentralblatt MATH identifier
1321.60209

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60K37: Processes in random environments

Keywords
spanning trees Brownian web Poisson point processes Poisson tree Coalescing processes Invariance Principle

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


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