The Brownian web: Characterization and convergence

• 成果类型: Article
• 署名作者: Fontes, LRG; Isopi, M; Newman, CM; Ravishankar, K
• 署名单位: Universidade de Sao Paulo; Sapienza University Rome; New York University; State University of New York (SUNY) System; University at Albany, SUNY
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000568
• 发表日期: 2004
• 页码: 2857-2883
• 关键词: stochastic flows; random-walks; motion; trees; paths

摘要

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 x R. We extend the earlier work of Arratia and of Toth 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.