Two-dimensional Poisson trees converge to the brownian web

P. A. Ferrari; L. R. G. Fontes; Xian-Yuan Wu

Annales de l'I.H.P. Probabilités et statistiques (2005)

  • Volume: 41, Issue: 5, page 851-858
  • ISSN: 0246-0203

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Ferrari, P. A., Fontes, L. R. G., and Wu, Xian-Yuan. "Two-dimensional Poisson trees converge to the brownian web." Annales de l'I.H.P. Probabilités et statistiques 41.5 (2005): 851-858. <http://eudml.org/doc/77870>.

@article{Ferrari2005,
author = {Ferrari, P. A., Fontes, L. R. G., Wu, Xian-Yuan},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {coalescing one-dimensional Brownian motions},
language = {eng},
number = {5},
pages = {851-858},
publisher = {Elsevier},
title = {Two-dimensional Poisson trees converge to the brownian web},
url = {http://eudml.org/doc/77870},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Ferrari, P. A.
AU - Fontes, L. R. G.
AU - Wu, Xian-Yuan
TI - Two-dimensional Poisson trees converge to the brownian web
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
PB - Elsevier
VL - 41
IS - 5
SP - 851
EP - 858
LA - eng
KW - coalescing one-dimensional Brownian motions
UR - http://eudml.org/doc/77870
ER -

References

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  2. [2] M.D. Donsker, An invariance principle for certain probability limit theorems, Mem. Amer. Math. Soc.6 (1951) 1-12. Zbl0042.37602MR40613
  3. [3] P.A. Ferrari, L.R.G. Fontes, X.-Y. Wu, Two-dimensional Poisson Trees converge to the Brownian web, math.PR/0304247. Zbl1073.60094
  4. [4] P.A. Ferrari, C. Landim, H. Thorisson, Poisson trees, succession lines and coalescing random walks, Ann. Inst. H. Poincaré40 (2004) 141-152. Zbl1042.60064MR2044812
  5. [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. Zbl1015.60099MR1905852
  6. [6] L.R.G. Fontes, M. Isopi, C.M. Newman, K. Ravishankar, The Brownian web, Proc. Nat. Acad. Sci. USA99 (25) (2002) 15888-15893. Zbl1069.60068MR1944976
  7. [7] L.R.G. Fontes, M. Isopi, C.M. Newman, K. Ravishankar, The Brownian web: characterization and convergence, Ann. Probab.32 (2004) 2857-2883. Zbl1105.60075MR2094432
  8. [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. [9] S. Gangopadhyay, R. Roy, A. Sarkar, Random oriented trees: a model of drainage networks, Ann. Appl. Probab.14 (2004) 1242-1266. Zbl1047.60098MR2071422
  10. [10] O. Kallenberg, Foundations of Modern Probability, Springer-Verlag, 1997. Zbl0892.60001MR1464694
  11. [11] H.B. Mann, A. Wald, On stochastic limit and order relations, Ann. Math. Statist.14 (1943) 217-226. Zbl0063.03774MR9261
  12. [12] Y.V. Prohorov, Convergence of random processes and limits theorems in probability theory, Theory Probab. Appl.1 (1956) 157-214. Zbl0075.29001MR84896
  13. [13] I. Rodriguez-Iturbe, A. Rinaldo, Fractal River Basins: Chance and Self-Organization, Cambridge University Press, New York, 1997. 
  14. [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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