Correlated Drainage Model

TL;DR

This paper introduces a random oriented tree model on a d-dimensional lattice that forms a forest with positive probability in three dimensions, contrasting with existing models that only form forests in higher dimensions.

Contribution

The paper presents a novel random tree model on a 3D lattice that can form a forest with positive probability, unlike previous models requiring higher dimensions.

Findings

Model forms a forest in 3D with positive probability

Contrasts with existing models that need d>3

Provides new insights into random tree structures in lattice models

Abstract

In this article we present an example of a random oriented tree model on d-dimensional lattice, that is a forest in d=3 with positive probability. This is in contrast with the other random tree models in the literature which are a forest only when d strictly greater than 3.