Two-dimensional Poisson trees converge to the brownian web
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 5, pp. 851-858. 
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     author = {Ferrari, P. A. and Fontes, L. R. G. and Wu, Xian-Yuan},
     title = {Two-dimensional {Poisson} trees converge to the brownian web},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {851--858},
     publisher = {Elsevier},
     volume = {41},
     number = {5},
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     doi = {10.1016/j.anihpb.2004.06.003},
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     zbl = {1073.60094},
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     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2004.06.003/}
}
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Ferrari, P. A.; Fontes, L. R. G.; Wu, Xian-Yuan. Two-dimensional Poisson trees converge to the brownian web. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 5, pp. 851-858. doi : 10.1016/j.anihpb.2004.06.003. http://archive.numdam.org/articles/10.1016/j.anihpb.2004.06.003/

[1] R. Arratia, Limiting point processes for rescalings of coalescing and annihilating random walks on Z d , Ann. Probab. 9 (1981) 909-936. | MR | Zbl

[2] M.D. Donsker, An invariance principle for certain probability limit theorems, Mem. Amer. Math. Soc. 6 (1951) 1-12. | MR | Zbl

[3] P.A. Ferrari, L.R.G. Fontes, X.-Y. Wu, Two-dimensional Poisson Trees converge to the Brownian web, math.PR/0304247.

[4] P.A. Ferrari, C. Landim, H. Thorisson, Poisson trees, succession lines and coalescing random walks, Ann. Inst. H. Poincaré 40 (2004) 141-152. | Numdam | MR | Zbl

[5] L.R.G. Fontes, M. Isopi, C.M. Newman, Random walks with strongly inhomogeneous rates and singular diffusions: convergence, localization and aging in one dimension, Ann. Probab. 30 (2002) 579-604. | MR | Zbl

[6] L.R.G. Fontes, M. Isopi, C.M. Newman, K. Ravishankar, The Brownian web, Proc. Nat. Acad. Sci. USA 99 (25) (2002) 15888-15893. | MR | Zbl

[7] L.R.G. Fontes, M. Isopi, C.M. Newman, K. Ravishankar, The Brownian web: characterization and convergence, Ann. Probab. 32 (2004) 2857-2883. | MR | Zbl

[8] L.R.G. Fontes, M. Isopi, C.M. Newman, D.L. Stein, Aging in 1D discrete spin models and equivalent systems, Phys. Rev. Lett. 87 (2001) 110201.

[9] S. Gangopadhyay, R. Roy, A. Sarkar, Random oriented trees: a model of drainage networks, Ann. Appl. Probab. 14 (2004) 1242-1266. | MR | Zbl

[10] O. Kallenberg, Foundations of Modern Probability, Springer-Verlag, 1997. | MR | Zbl

[11] H.B. Mann, A. Wald, On stochastic limit and order relations, Ann. Math. Statist. 14 (1943) 217-226. | MR | Zbl

[12] Y.V. Prohorov, Convergence of random processes and limits theorems in probability theory, Theory Probab. Appl. 1 (1956) 157-214. | MR | Zbl

[13] I. Rodriguez-Iturbe, A. Rinaldo, Fractal River Basins: Chance and Self-Organization, Cambridge University Press, New York, 1997.

[14] A.E. Scheidegger, A stochastic model for drainage patterns into an intramontane trench, Bull. Ass. Sci. Hydrol. 12 (1967) 15-20.

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