Reconstructing the environment seen by a RWRE. (English) Zbl 1312.60119

Summary: 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.


60K37 Processes in random environments
60G50 Sums of independent random variables; random walks
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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