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- W4297812953 abstract "Motivated by [G. Cannizzaro, M. Hairer, Comm. Pure Applied Math., '22], we provide a construction of the Brownian Web (see [T'oth B., Werner W., Probab. Theory Related Fields, '98] and [L. R. G. Fontes, M. Isopi, C. M. Newman, and K. Ravishankar, Ann. Probab., '04]), i.e. a family of coalescing Brownian motions starting from every point in $mathbb R^2$, as a random variable taking values in the space of (spatial) $mathbb R$-trees. This gives a stronger topology than the classical one {(i.e. Hausdorff convergence on closed sets of paths)}, thus providing us with more continuous functions of the Brownian Web and ruling out a number of potential pathological behaviours. Along the way, we introduce a modification of the topology of spatial $mathbb R$-trees in [T. Duquesne, J.-F. Le Gall, Probab. Theory Related Fields, '05] and [M. T. Barlow, D. A. Croydon, T. Kumagai, Ann. Probab. '17] which makes it a complete separable metric space and could be of independent interest. We determine some properties of the characterisation of the Brownian Web in this context (e.g. its box-counting dimension) and recover some which were determined in earlier works, such as duality, special points and convergence of the graphical representation of coalescing random walks." @default.
- W4297812953 created "2022-10-01" @default.
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- W4297812953 date "2021-02-08" @default.
- W4297812953 modified "2023-09-23" @default.
- W4297812953 title "The Brownian Web as a random $mathbb R$-tree" @default.
- W4297812953 doi "https://doi.org/10.48550/arxiv.2102.04068" @default.
- W4297812953 hasPublicationYear "2021" @default.
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