THE 2D-DIRECTED SPANNING FOREST CONVERGES TO THE BROWNIAN WEB

Authors

David Coupier, Université de Lille
Kumarjit Saha, Ashoka University
Anish Sarkar, Indian Statistical Institute, Kolkata
Viet Chi Tran, Université Gustave Eiffel

Article Type

Research Article

Publication Title

Annals of Probability

Abstract

The two-dimensional directed spanning forest (DSF) introduced by Baccelli and Bordenave is a planar directed forest whose vertex set is given by a homogeneous Poisson point process N on R2. If the DSF has direction −ey, the ancestor h(u) of a vertex u ε N is the nearest Poisson point (in the L 2 distance) having strictly larger y-coordinate. This construction induces complex geometrical dependencies. In this paper, we show that the collection of DSF paths, properly scaled, converges in distribution to the Brownian web (BW). This verifies a conjecture made by Baccelli and Bordenave in 2007 (Ann. Appl. Probab. 17 (2007) 305–359).

First Page

435

Last Page

484

DOI

10.1214/20-AOP1478

Publication Date

1-1-2021

Comments

Open Access, Green

Recommended Citation

Coupier, David; Saha, Kumarjit; Sarkar, Anish; and Tran, Viet Chi, "THE 2D-DIRECTED SPANNING FOREST CONVERGES TO THE BROWNIAN WEB" (2021). Journal Articles. 2128.
https://digitalcommons.isical.ac.in/journal-articles/2128