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October 2004 The Brownian web: Characterization and convergence
L. R. G. Fontes, M. Isopi, C. M. Newman, K. Ravishankar
Ann. Probab. 32(4): 2857-2883 (October 2004). DOI: 10.1214/009117904000000568


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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L. R. G. Fontes. M. Isopi. C. M. Newman. K. Ravishankar. "The Brownian web: Characterization and convergence." Ann. Probab. 32 (4) 2857 - 2883, October 2004.


Published: October 2004
First available in Project Euclid: 8 February 2005

zbMATH: 1105.60075
MathSciNet: MR2094432
Digital Object Identifier: 10.1214/009117904000000568

Primary: 60D05 , 60F17 , 60J65 , 60K35 , 82B41

Keywords: Brownian networks , Brownian web , Coalescing random walks , continuum limit , invariance principle

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 4 • October 2004
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