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 ?×?. 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.
The Brownian Web: Convergence and Characterisation / Fontes, L. R.; Isopi, Marco; Newman, C. M.; Ravishankar, K.. - In: ANNALS OF PROBABILITY. - ISSN 0091-1798. - STAMPA. - 32:(2004), pp. 2857-2884. [10.1214/009117904000000568]
The Brownian Web: Convergence and Characterisation
ISOPI, Marco;
2004
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 ?×?. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
