Two-dimensional Poisson trees converge to the brownian web

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

doi:10.1016/j.anihpb.2004.06.003

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

Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 5, pp. 851-858

MR Zbl | 1 citation dans Numdam

DOI : 10.1016/j.anihpb.2004.06.003

@article{AIHPB_2005__41_5_851_0,
     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},
     year = {2005},
     publisher = {Elsevier},
     volume = {41},
     number = {5},
     doi = {10.1016/j.anihpb.2004.06.003},
     mrnumber = {2165253},
     zbl = {1073.60094},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpb.2004.06.003/}
}

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
SP  - 851
EP  - 858
VL  - 41
IS  - 5
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpb.2004.06.003/
DO  - 10.1016/j.anihpb.2004.06.003
LA  - en
ID  - AIHPB_2005__41_5_851_0
ER  -

%0 Journal Article
%A Ferrari, P. A.
%A Fontes, L. R. G.
%A Wu, Xian-Yuan
%T Two-dimensional Poisson trees converge to the brownian web
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2005
%P 851-858
%V 41
%N 5
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpb.2004.06.003/
%R 10.1016/j.anihpb.2004.06.003
%G en
%F AIHPB_2005__41_5_851_0

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

Bibliographie
Cité par

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

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

[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. | Zbl | MR | Numdam

[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. | Zbl | MR

[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. | Zbl | MR

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

[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. | Zbl | MR

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

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

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

[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.

Cité par Sources :