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) no. 2, pp. 263-285. 
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     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},
     pages = {263--285},
     publisher = {Elsevier},
     volume = {39},
     number = {2},
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     doi = {10.1016/S0246-0203(02)00002-X},
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     zbl = {1017.60105},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/S0246-0203(02)00002-X/}
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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) no. 2, pp. 263-285. doi : 10.1016/S0246-0203(02)00002-X. http://archive.numdam.org/articles/10.1016/S0246-0203(02)00002-X/

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

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

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

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

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

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

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

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

[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

[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 | Zbl

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

[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

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

[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 | Zbl

[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 | Zbl

[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

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

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