Matrix analysis
Detecting defects in periodic scenery by random walks on Z
Random Structures & Algorithms
Random Structures & Algorithms
Reconstructing a three-color scenery by observing it along a simple random walk path
Random Structures & Algorithms
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Suppose that attached to each site z ∈ Z is a coin with bias θ(z), and only finitely many of these coins have nonzero bias. Allow a simple random walker to generate observations by tossing, at each move, the coin attached to its current position. Then we can determine the biases {θ(z)}z∈Z, using only the outcomes of these coin tosses and no information about the path of the random walker, up to a shift and reflection of Z. This generalizes a result of Harris and Keane.