TY - JOUR
T1 - The Brownian Web
AU - Fontes, L. R.G.
AU - Isopi, M.
AU - Newman, C. M.
AU - Ravishankar, K.
PY - 2002/12/10
Y1 - 2002/12/10
N2 - Arratia, [Arratia, R. (1979) Ph.D. thesis (University of Wisconsin, Madison) and unpublished work] and later Toth and Werner [Toth, B. & Werner, W. (1998) Probab. Theory Relat. Fields 111, 375-452] 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 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.
AB - Arratia, [Arratia, R. (1979) Ph.D. thesis (University of Wisconsin, Madison) and unpublished work] and later Toth and Werner [Toth, B. & Werner, W. (1998) Probab. Theory Relat. Fields 111, 375-452] 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 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.
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U2 - 10.1073/pnas.252619099
DO - 10.1073/pnas.252619099
M3 - Article
C2 - 12451173
AN - SCOPUS:0037059056
SN - 0027-8424
VL - 99
SP - 15888
EP - 15893
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 25
ER -