"Random directed forest and the Brownian web" by Rahul Roy, Kumarjit Saha et al.
 

Random directed forest and the Brownian web

Article Type

Research Article

Publication Title

Annales de l'institut Henri Poincare (B) Probability and Statistics

Abstract

Consider the d dimensional lattice Zd where each vertex is open or closed with probability p or 1 - p respectively. An open vertex u := (u(1), u(2),...,u(d)) is connected by an edge to another open vertex which has the minimum L1 distance among all the open vertices x with x(d) > u(d). It is shown that this random graph is a tree almost surely for d = 2 and 3 and it is an infinite collection of disjoint trees for d ≥4. In addition, for d = 2, we show that when properly scaled, the family of its paths converges in distribution to the Brownian web.

First Page

1106

Last Page

1143

DOI

10.1214/15-AIHP672

Publication Date

8-1-2016

Comments

Open Access; Green Open Access

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