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This is a continuation of our earlier work [Stochastic Processes and theirApplications, 129(1), pp.102--128, 2019] on the random walk in random sceneryand in random layered conductance. We complete the picture of upper deviationof the random walk in random scenery, and also prove a bound on lower deviationprobability. Based on these results, we determine asymptotics of the returnprobability, a certain moderate deviation probability, and the Green functionof the random walk in random layered conductance.

Quenched tail estimate for the random walk in random scenery and in random layered conductance II