The Brownian Web
Probability
2009-11-07 v2 Condensed Matter
Mathematical Physics
math.MP
Abstract
Arratia, and later T\'oth and Werner, constructed random processes that formally correspond to coalescing one-dimensional Brownian motions starting from every space-time point. We extend their work by constructing and characterizing what we call the {\em Brownian Web} as a random variable taking values in an appropriate (metric) space whose points are (compact) sets of paths. This leads to general convergence criteria and, in particular, to convergence in distribution of coalescing random walks in the scaling limit to the Brownian Web.
Cite
@article{arxiv.math/0203184,
title = {The Brownian Web},
author = {L. R. G. Fontes and M. Isopi and C. M. Newman and K. Ravishankar},
journal= {arXiv preprint arXiv:math/0203184},
year = {2009}
}
Comments
A few changes were made in Section 1, including the addition of some comments and a Remark just before and after Theorem 1.1