Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 10 (2005), paper no. 5, 36-44.
On the Zero-One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment
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.
Electron. Commun. Probab., Volume 10 (2005), paper no. 5, 36-44.
Accepted: 4 March 2005
First available in Project Euclid: 4 June 2016
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Rassoul-Agha, Firas. On the Zero-One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment. Electron. Commun. Probab. 10 (2005), paper no. 5, 36--44. doi:10.1214/ECP.v10-1130. https://projecteuclid.org/euclid.ecp/1465058070