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On the zero-one law and the law of large numbers for random walk in mixing random environment. (English) Zbl 1060.60101

Summary: 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.

MSC:

60K37 Processes in random environments
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
60F20 Zero-one laws
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