 |
|
|
| | | | | |
|
|
|
|
|
On the Zero-One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment
|
Firas Rassoul-Agha, Ohio State University, USA
|
Abstract
We prove a weak version of the law of large numbers
for multi-dimensional finite range
random walks in certain mixing elliptic random environments.
This already improves previously existing results, where a law of large numbers
was known only under strong enough transience.
We also prove that for such walks the zero-one law implies a law of large numbers.
|
Full text: PDF
Pages: 36-44
Published on: March 4, 2005
|
Bibliography
| Alili, S. Asymptotic behaviour for random walks in random environments.
J. Appl. Probab. 36 (1999), no. 2, 334--349. MR1724844 (2000i:60120) |
| Comets, F. and Zeitouni, O. A law of large numbers for random walks in random mixing environments.
Ann. Probab. 32 (2004), no. 1B, 880--914. MR2039946 |
| Dobrushin, R. L. and Shlosman, S. B. Completely analytical Gibbs fields.
Statistical physics and dynamical systems (Köszeg, 1984),
371--403, Progr. Phys., 10, Birkhäuser Boston, Boston, MA, 1985. MR0821307 (87d:82007) |
| Georgii, H.-O. Gibbs measures and phase transitions.
de Gruyter Studies in Mathematics, 9. Walter de Gruyter & Co., Berlin, 1988. xiv+525 pp. ISBN: 0-89925-462-4 MR0956646 (89k:82010) |
| Kalikow, S. A. Generalized random walk in a random environment.
Ann. Probab. 9 (1981), no. 5, 753--768. MR0628871 (84c:60101) |
| Rassoul-Agha, F. The point of view of the particle on the law of large numbers for random walks in a mixing random environment.
Ann. Probab. 31 (2003), no. 3, 1441--1463. MR1989439 (2004h:60151) |
| Rassoul-Agha, F. Large deviations for random walks in a mixing random environment and other (non-Markov) random walks.
Comm. Pure Appl. Math. 57 (2004), no. 9, 1178--1196. MR2059678 (2005b:60067) |
| Solomon, F. Random walks in a random environment.
Ann. Probability 3 (1975), 1--31. MR0362503 (50 #14943) |
| Sznitman, A.-S. An effective criterion for ballistic behavior of random walks in random environment.
Probab. Theory Related Fields 122 (2002), no. 4, 509--544. MR1902189 (2003c:60168) |
| Sznitman, A.-S. and Zerner, M. A law of large numbers for random walks in random environment.
Ann. Probab. 27 (1999), no. 4, 1851--1869. MR1742891 (2001f:60116) |
| Varadhan, S. R. S. Large deviations for random walks in a random environment.
Dedicated to the memory of Jürgen K. Moser.
Comm. Pure Appl. Math. 56 (2003), no. 8, 1222--1245. MR1989232 (2004d:60073) |
| Zerner, M. P. W. A non-ballistic law of large numbers for random walks in i.i.d. random environment.
Electron. Comm. Probab. 7 (2002), 191--197 (electronic). MR1937904 (2003h:60149) |
| Zerner, M. P. W. and Merkl, F. A zero-one law for planar random walks in random environment.
Ann. Probab. 29 (2001), no. 4, 1716--1732. MR1880239 (2003a:60144) |
|
|
|
|
|
|
|
|
| | | | |
Electronic Communications in Probability. ISSN: 1083-589X |
|
Context