The Brownian web: Characterization and convergence

L. R.G. Fontes; M. Isopi; C. M. Newman; K. Ravishankar

doi:10.1214/009117904000000568

The Brownian web: Characterization and convergence

L. R.G. Fontes, M. Isopi, C. M. Newman, K. Ravishankar

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The Brownian web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in ℝ × ℝ. We extend the earlier work of Arratia and of Tóth and Werner by providing a new characterization which is then used to obtain convergence results for the BW distribution, including convergence of the system of all coalescing random walks to the BW under diffusive space-time scaling.

Original language	English (US)
Pages (from-to)	2857-2883
Number of pages	27
Journal	Annals of Probability
Volume	32
Issue number	4
DOIs	https://doi.org/10.1214/009117904000000568
State	Published - Oct 2004

Keywords

Brownian networks
Brownian web
Coalescing random walks
Continuum limit
Invariance principle

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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author = "Fontes, {L. R.G.} and M. Isopi and Newman, {C. M.} and K. Ravishankar",

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AU - Newman, C. M.

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AB - The Brownian web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in ℝ × ℝ. We extend the earlier work of Arratia and of Tóth and Werner by providing a new characterization which is then used to obtain convergence results for the BW distribution, including convergence of the system of all coalescing random walks to the BW under diffusive space-time scaling.

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KW - Coalescing random walks

KW - Continuum limit

KW - Invariance principle

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JF - Annals of Probability

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The Brownian web: Characterization and convergence

Abstract

Keywords

ASJC Scopus subject areas

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