Scaling limit for a drainage network model

2008/09/19 by Cristian F. Coletti, C. F. Coletti, E. S. Dias +6 · 1 citation
Mathematics · #60F17 #60K35 #60K40 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60F17 #msc:60K35 #msc:60K40

paper · pdf · doi:10.48550/arxiv.0809.3454

15 pages

arxiv created 2008/09/19 · openalex publication_date 2008/09/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Throughput in inhomogeneous planar drainage networks

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