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

Gantert, Nina; Nagel, Jan

Electron. Commun. Probab. 19, Paper No. 27, 9 p. (2014).

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.

MSC:

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

Keywords:

random walk; random environment; scenery reconstruction