The point of view of the particle on the law of large numbers for random walks in a mixing random environment

Annals of Probability

Volumn 31, Issue 3, 2003, Pages 1441-1463

  Rassoul Agha, Firas ^a,b  

^a NEW YORK UNIVERSITY   (United States)

^b OHIO STATE UNIVERSITY   (United States)

Author keywords

Dobrushin Shlosman mixing; Kalikow's condition; Law of large numbers; Point of view of the particle; Random environments; Random walks

Indexed keywords

EID: 0038034723     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1055425786     Document Type: Article

References (20)

1. ALILI, S. (1999). Asymptotic behaviour for random walks in random environments. J. Appl. Probab. 36 334-349.
2. BOLTHAUSEN, E. and SZNITMAN, A.-S. (2003). On the static and dynamic points of view for certain random walks in random environment. Methods Appl. Anal. 8. To appear.
3. COMETS, F. and ZEITOUNI, O. (2002). A law of large numbers for random walks in random mixing environments. Preprint. Available at www.arXiv.org.
4. DE MASI, A., FERRARI, P. A., GOLDSTEIN, S. and WICK, W. D. (1989). An invariance principle for reversible Markov processes with applications to random motions in random environments. J. Statist. Phys. 55 787-855.
5. DOBRUSHIN, R. L. and SHLOSMAN, S. B. (1985). Constructive criterion for the uniqueness of a Gibbs field. In Statistical Physics and Dynamical Systems (J. Fritz, A. Jaffe and D. Szasz, eds.) 347-370. Birkhäuser, Boston.
6. DOBRUSHIN, R. L. and SHLOSMAN, S. B. (1985). Completely analytical Gibbs fields. In Statistical Physics and Dynamical Systems (J. Fritz, A. Jaffe and D. Szasz, eds.) 371-403. Birkhäuser, Boston.
7. GEORGII, H. O. (1988). Gibbs Measures and Phase Transitions, de Gruyter, Berlin.
8. KALIKOW, S. A. (1981). Generalized random walk in a random environment. Ann. Probab. 9 753-768.
9. KIPNIS, C. and VARADHAN, S. R. S. (1986). A central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusion. Comm. Math. Phys. 104 1-19.
10. KOMOROWSKI, T. and KRUPA, G. (2003). The law of large numbers for ballistic, multidimensional random walks on random lattices with correlated sites. Ann. Inst. H. Poincaré Probab. Statist. To appear.
11. KOZLOV, S. M. (1985). The averaging method and walks in inhomogeneous environments. Russian Math. Surveys 40 73-145.
12. LAWLER, G. F. (1982). Weak convergence of a random walk in a random environment. Comm. Math. Phys. 87 81-87.
13. OLLA, S. (1994). Lectures on Homogenization of Diffusion Processes in Random Fields. Ecole Polytechnique, Palaiseau.
14. PAPANICOLAOU, G. and VARADHAN, S. R. S. (1981). Boundary value problems with rapidly oscillating random coefficients. In Random Fields 835-873. North-Holland, Amsterdam.
15. SOLOMON, F. (1975). Random walks in a random environment. Ann. Probab. 3 1-31.
16. SZNITMAN, A.-S. (2000). Lectures on random motions in random media. Preprint. Available at www.math.ethz.ch/̃sznitman/lectures.ps.
17. SZNITMAN, A.-S. (2002). An effective criterion for ballistic behavior of random walks in random environment. Probab. Theory Related Fields 122 509-544.
18. SZNITMAN, A.-S. and ZERNER, M. (1999). A law of large numbers for random walks in random environment. Ann. Probab. 27 1851-1869.
19. ZEITOUNI, O. (2001). Saint Flour lecture notes on random walks in random environments. Preprint. Available at www-ee.technion.ac.il/̃zeitouni.
20. ZERNER, M. and MERKL, F. (2001). A zero-one law for planar random walks in random environment. Ann. Probab. 29 1716-1732.