Asymptotic properties of certain anisotropic walks in random media

Annals of Applied Probability

Volumn 12, Issue 2, 2002, Pages 477-510

  Shen, Lian ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Asymptotic random walks; Ballistic walks; Random media

Indexed keywords

EID: 0036335638     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1026915612     Document Type: Article

References (18)

1. CARNE, T. K. (1985). A transmutation formula for Markov chains. Bull. Sci. Math. 109 399-405.
2. DE MASI, A., FERRARI, P. A., GOLDSTEIN, S. and WICK, W. D. (1989). An invariance principle for reversible Markov processes. Applications to random motions in random environments. J. Statist. Phys. 55 787-855.
3. DIEUDONNÉ, J. (1960). Foundations of Modern Analysis 1. Academic Press, New York.
4. DURRETT, R. (1996). Probability: Theory and Examples, 2nd ed. Wadsworth & Brooks/Cole, Belmont, CA.
5. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes. Wiley, New York.
6. HAVLIN, S. and BUNDE, A. (1991). Transport in the presence of additional physical constraints. In Fractals and Disordered Systems (A. Bunde and S. Havlin, eds.). Springer, Berlin.
7. KALIKOW, S. A. (1981). Generalized random walk in a random environment. Ann. Probab. 9 753-768.
8. KOZLOV, S. M. (1985). The method of averaging and walks in inhomogeneous environments. Russian Math. Surveys 40 73-145.
9. LAWLER, G. F. (1982). Weak convergence of a random walk in a random environment. Comm. Math. Phys. 87 81-87.
10. LEBOWITZ, J. L. and ROST, H. (1994). The Einstein relation for the displacement of a test particle in a random environment. Stochastic Process. Appl. 54 183-196.
11. NUMMELIN, E. (1984). General Irreducible Markov Chains and Nonnegative Operators. Cambridge Univ. Press.
12. OLLA, S. (1994). Homogenization of diffusion processes in random fields. Ecole Doctorale, Ecole Polytechnique, Palaiseau.
13. PAPANICOLAOU, G. and VARADHAN, S. R. S. (1981). Boundary value problems with rapidly oscillating random coefficients. In Random Fields (J. Fritz and D. Szasz, eds.). North-Holland, Amsterdam.
14. REED, M. and SIMON, B. (1980). Methods of Modern Mathematical Physics, Functional Analysis, rev. ed. Academic Press, New York.
15. REVUZ, D. (1975). Markov Chains. North-Holland, Amsterdam.
16. SZNITMAN, A.-S. (2000). Slowdown estimates and central limit theorem for random walks in random environment. J. Eur. Math. Soc. 2 93-143.
17. BOLTHAUSEN, E. and SZNITMAN, A.-S. (2000). Lectures in Random Media. Birkhäuser, Basel.
18. SZNITMAN, A.-S. and ZERNER, M. P. W. (1999). A law of large numbers for random walks in random environment. Ann. Probab. 27 1851-1869.