The Brownian web: Characterization and convergence

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)2857-2883
Number of pages27
JournalAnnals of Probability
Volume32
Issue number4
DOIs
StatePublished - 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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