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The Brownian web. (English) Zbl 1069.60068

R. Arratia [Ph.D. thesis (University of Wisconsin, Madison, 1979) and unpublished work] and later B. Tóth and W. Werner [Probab. Theory Relat. Fields 111, No. 3, 375–452 (1998; Zbl 0912.60056)] 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.

MSC:

60J65 Brownian motion

Citations:

Zbl 0912.60056
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References:

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