Quenched trap model for Lévy flights

In this paper we introduce a quenched trap model for Lévy flights. It describes the dynamics of Lévy flights in a fixed time random environment. Our main result is the derivation of the long-time limit of the introduced process, which reveals its anomalous scaling. We also analyze the asymptotic behavior of other objects related to this model, such as the coverage time. We illustrate the theoretical findings by extended Monte Carlo simulations using the proposed numerical scheme.