## Uniqueness of the mixing measure for a random walk in a random environment on the positive integers.(English)Zbl 1189.60189

Summary: Consider a random walk in an irreducible random environment on the positive integers. We prove that the annealed law of the random walk determines uniquely the law of the random environment. An application to linearly edge-reinforced random walk is given.

### MSC:

 60K37 Processes in random environments 60K35 Interacting random processes; statistical mechanics type models; percolation theory

### Keywords:

random walk in a random environment; mixing measure
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