This is a continuation of our earlier work [Stochastic Processes and their Applications, 129(1), pp.102–128, 2019] on the random walk in random scenery and in random layered conductance. We complete the picture of upper deviation of the random walk in random scenery, and also prove a bound on lower deviation probability. Based on these results, we determine asymptotics of the return probability, a certain moderate deviation probability, and the Green function of the random walk in random layered conductance.
Jean-Dominique Deuschel. Ryoki Fukushima. "Quenched tail estimate for the random walk in random scenery and in random layered conductance II." Electron. J. Probab. 25 1 - 28, 2020. https://doi.org/10.1214/20-EJP478