Scaling limit for a drainage network model

TL;DR

This paper proves that the rescaled paths of a 2D drainage network model converge to the Brownian web, demonstrating a scaling limit for the network's structure.

Contribution

It establishes the convergence of a 2D drainage network model's paths to the Brownian web, extending understanding of such models' scaling behavior.

Findings

Rescaled paths converge to the Brownian web

Verification of convergence criteria for the model

Provides a rigorous mathematical framework for the scaling limit

Abstract

We consider the two dimensional version of a drainage network model introduced by Gangopadhyay, Roy and Sarkar, and show that the appropriately rescaled family of its paths converges in distribution to the Brownian web. We do so by verifying the convergence criteria proposed by Fontes, Isopi, Newman and Ravishankar.