### Reconstructing the environment seen by a RWRE

**Nina Gantert**

*(Technische Universität München)*

**Jan Nagel**

*(Technische Universität München)*

#### Abstract

Consider a walker performing a random walk in an i.i.d. random environment, and assume that the walker tells us at each time the environment it sees at its present location. Given this history of the transition probabilities seen from the walker - but not its trajectory - can we reconstruct the law of the environment? We show that in a one-dimensional environment, the law of the environment can be reconstructed. This model can be seen as a special case of a scenery reconstruction problem, where the steps of the random walker depend on the scenery.

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Pages: 1-9

Publication Date: May 7, 2014

DOI: 10.1214/ECP.v19-3013

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