Electronic Communications in Probability

Reconstructing the environment seen by a RWRE

Nina Gantert and Jan Nagel

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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.<br />

Article information

Electron. Commun. Probab., Volume 19 (2014), paper no. 27, 9 pp.

Accepted: 7 May 2014
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

random walk in random environment scenery reconstruction

This work is licensed under a Creative Commons Attribution 3.0 License.


Gantert, Nina; Nagel, Jan. Reconstructing the environment seen by a RWRE. Electron. Commun. Probab. 19 (2014), paper no. 27, 9 pp. doi:10.1214/ECP.v19-3013. https://projecteuclid.org/euclid.ecp/1465316729

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