THE 2D-DIRECTED SPANNING FOREST CONVERGES TO THE BROWNIAN WEB
成果类型：
Article
署名作者：
Coupier, David; Saha, Kumarjit; Sarkar, Anish; Viet Chi Tran
署名单位：
Universite de Lille; IMT - Institut Mines-Telecom; IMT Nord Europe; Ashoka University; Indian Statistical Institute; Indian Statistical Institute Bangalore; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); Universite Gustave-Eiffel
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/20-AOP1478
发表日期：
2021
页码：
435-484
关键词：
摘要：
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 R-2. If the DSF has direction -e(y), the ancestor h(u) of a vertex u is an element of 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).
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