The law of large numbers for ballistic, multi-dimensional random walks on random lattices with correlated sites
Komorowski, Tomasz ; Krupa, Grzegorz
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003), p. 263-285 / Harvested from Numdam
@article{AIHPB_2003__39_2_263_0,
     author = {Komorowski, Tomasz and Krupa, Grzegorz},
     title = {The law of large numbers for ballistic, multi-dimensional random walks on random lattices with correlated sites},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {39},
     year = {2003},
     pages = {263-285},
     doi = {10.1016/S0246-0203(02)00002-X},
     mrnumber = {1962136},
     zbl = {1017.60105},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2003__39_2_263_0}
}
Komorowski, Tomasz; Krupa, Grzegorz. The law of large numbers for ballistic, multi-dimensional random walks on random lattices with correlated sites. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) pp. 263-285. doi : 10.1016/S0246-0203(02)00002-X. http://gdmltest.u-ga.fr/item/AIHPB_2003__39_2_263_0/

[1] S. Alili, Asymptotic behaviour for random walks in random environments, J. Appl. Probab. 36 (1999) 334-349. | MR 1724844 | Zbl 0946.60046

[2] N. Alon, J. Spencer, P. Erdös, The Probabilistic Method, Wiley, New York, 1992. | MR 1140703 | Zbl 0767.05001

[3] D. Boivin, Weak convergence for reversible random walks in a random environment, Ann. Probab. 21 (1993) 1427-1440. | MR 1235423 | Zbl 0783.60067

[4] J. Bricmont, A. Kupiainen, Random walks in asymmetric random environments, Comm. Math. Phys. 142 (1991) 345-420. | MR 1137068 | Zbl 0734.60112

[5] R. Durrett, Probability Theory and Examples, Wadsworth and Brooks/Cole, Pacific Grove, CA, 1991. | MR 1068527 | Zbl 0709.60002

[6] S.M. Kozlov, The method of averaging and walks in inhomogeneous environments, Russian Math. Surveys 40 (1985) 73-145. | MR 786087 | Zbl 0615.60063

[7] A. Lasota, M. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press, 1985. | MR 832868 | Zbl 0606.58002

[8] G.F. Lawler, Weak convergence of a random walk in a random environment, Comm. Math. Phys. 87 (1982) 81-87. | MR 680649 | Zbl 0502.60056

[9] S.A. Molchanov, Lectures on Random Media. Ecole d'été de probabilités de St. Flour XXII, Lecture Notes in Math., 1581, Springer, Berlin, 1994, pp. 242-411. | Zbl 0814.60093

[10] S. Olla, Homogenization of Diffusion Processes in Random Fields, Manuscript of Centre de Mathématiques Appliquées, 1994.

[11] G.C. Papanicolaou, S.R.S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, in: Fritz J., Lebowitz J.L. (Eds.), Random Fields Coll., Math. Soc. Janos Bolyai., 27, North Holland, Amsterdam, 1982, pp. 835-873. | MR 712714 | Zbl 0499.60059

[12] A.Yu. Rozanov, Stationary Random Processes, Holden-Day, 1969. | MR 214134 | Zbl 0152.16302

[13] L. Shen, A law of large numbers and a central limit theorem for biased random motions in random environment, Preprint, 2000.

[14] A.V. Skorokhod, σ-algebras of events on probability spaces. Similarity and factorization, Theory Probab. Appl. 36 (1990) 63-73. | Zbl 0745.60004

[15] A.S. Sznitman, An effective criterion for ballistic behavior of random walks in random environment, Preprint, 2000. | MR 1902189

[16] A.S. Sznitman, Slowdown estimates and central limit theorem for random walks in random environment, J. Eur. Math. Soc. 2 (2000) 93-143. | MR 1763302 | Zbl 0976.60097

[17] A.S. Sznitman, Lectures on random motions in random media, 2000, Preprint available at http://www.math.ethz.ch/~sznitman/preprint.shtml.

[18] A.S. Sznitman, M. Zerner, A law of large numbers for random walks in random environment, Ann. Probab. 27 (1999) 1851-1869. | MR 1742891 | Zbl 0965.60100

[19] O. Zeitouni, Lecture notes on random walks in random environments, 2001, Preprint available at , http://www-ee.technion.ac.il/zeitouni/ps/notes1.ps. | MR 2071631

[20] M. Zerner, Lyapunov exponents and quenched large deviation for multidimensional random walk in random environment, Ann. Probab. 26 (1998) 1446-1476. | MR 1675027 | Zbl 0937.60095