Convergence to the brownian Web for a generalization of the drainage network model
Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 3, pp. 899-919.

We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing paths that can cross each other and are dependent even before coalescence. We show that under diffusive scaling this system converges in distribution to the Brownian Web.

Nous introduisons un système de marches aléatoires coalescentes unidimensionnelles, avec des sauts à longue portée. Ce système autorise des chemins qui se croisent, et qui sont dépendants, même avant leur coalescence. Après une renormalisation diffusive, nous montrons que ce système converge en loi vers le réseau brownien.

DOI: 10.1214/13-AIHP544
Classification: 60K35
Keywords: brownian web, coalescing brownian motions, coalescing random walks, drainage network, scaling limit, invariance principle, interacting particle systems
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Coletti, Cristian; Valle, Glauco. Convergence to the brownian Web for a generalization of the drainage network model. Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 3, pp. 899-919. doi : 10.1214/13-AIHP544. http://archive.numdam.org/articles/10.1214/13-AIHP544/

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