Scenery reconstruction for random walk on random scenery systems

Consider a simple random walk on ℤ with coloring of ℤ. Look at the sequence first N steps taken in walk, together colors visited locations. We call this record. From record one can deduce interval that was visited, which is size approximately $$\sqrt $$ . This called scenery reconstruction. Now suppose an adversary may change δN entries obtained. What we from about now? In paper show it likely still reconstruct large part scenery. More precisely, for any θ <0.5, p > 0 and ∊ 0, there are N0 δ0 such if δ < δ0, then probability 1 − Nθ integers scenery, up to having number suggested reconstructions less than 2∊s, where s whose color reconstruct.