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We consider one infinite path of a Random Walk in Random Environment (RWRE,for short) in an unknown environment. This environment consists of eitheri.i.d.\ site or bond randomness. At each position the random walker stops andtells us the environment it sees at the point where it is, without telling us,where it is. These observations $\chi'$ are spoiled by reading errors thatoccur with probability $p<1$. We show: If the RWRE is recurrent and satisfiesthe standard assumptions on such RWREs, then with probability one in theenvironment, the errors, and the random walk we are able reconstruct the law ofthe environment. For most situations this result is even independent of thevalue of $p$. If the distribution of the environment has a non-atomic part, wecan even reconstruct the environment itself, up to translation.

Reconstructing a (recurrent) random environment from a single trajectory of Random Walk in Random Environment with errors