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.
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