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N2 - Arratia, [Arratia, R. (1979) Ph.D. thesis (University of Wisconsin, Madison) and unpublished work] and later Toth and Werner [Toth, B. & Werner, W. (1998) Probab.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AB - Arratia, [Arratia, R. (1979) Ph.D. thesis (University of Wisconsin, Madison) and unpublished work] and later Toth and Werner [Toth, B. & Werner, W. (1998) Probab.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 -