The problem of finding the best path in a random medium is investigated. If the random medium is allowed to undergo slow drifts, the best path can be drastically different. The scaling of the excited states is also discussed. A host of new exponents are found for the 2d problem. The implications for the growing surfaces are also pointed out.

• Received 2 July 1987

DOI:https://doi.org/10.1103/PhysRevLett.59.2125