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Scaling Limit for a Drainage Network Model

Part of:Special processesLimit theorems

Published online by Cambridge University Press:  14 July 2016

C. F. Coletti,
L. R. G. Fontes and
E. S. Dias
C. F. Coletti*
Affiliation:
Universidade de São Paulo
L. R. G. Fontes*
Affiliation:
Universidade de São Paulo
E. S. Dias*
Affiliation:
Universidade de São Paulo
*
∗ Postal address: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090, São Paulo, Brazil.
∗ Postal address: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090, São Paulo, Brazil.
∗ Postal address: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, 05508-090, São Paulo, Brazil.
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Abstract

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We consider the two-dimensional version of a drainage network model introduced in Gangopadhyay, Roy and Sarkar (2004), 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 in Fontes, Isopi, Newman and Ravishankar (2002).

Keywords

Drainage networkcoalescing random walkBrownian webcoalescing Brownian motion

MSC classification

Secondary:60K35: Interacting random processes; statistical mechanics type models; percolation theory60K40: Other physical applications of random processes60F17: Functional limit theorems; invariance principles

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 4 , December 2009, pp. 1184 - 1197
Copyright
Copyright © Applied Probability Trust 2009 

Footnotes

Research supported by FAPESP grant 2006/54511-2.

Research supported by FAPESP grant 2004/13008-0.

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