The Annals of Probability

The Brownian web: Characterization and convergence

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

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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.

Article information

Source
Ann. Probab., Volume 32, Number 4 (2004), 2857-2883.

Dates
First available in Project Euclid: 8 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1107883340

Digital Object Identifier
doi:10.1214/009117904000000568

Mathematical Reviews number (MathSciNet)
MR2094432

Zentralblatt MATH identifier
1105.60075

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J65: Brownian motion [See also 58J65] 60F17: Functional limit theorems; invariance principles 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41] 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

Keywords
Brownian web invariance principle coalescing random walks Brownian networks continuum limit

Citation

Fontes, L. R. G.; Isopi, M.; Newman, C. M.; Ravishankar, K. The Brownian web: Characterization and convergence. Ann. Probab. 32 (2004), no. 4, 2857--2883. doi:10.1214/009117904000000568. https://projecteuclid.org/euclid.aop/1107883340


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