Nonlinear dynamics of continuous-time random walks in inhomogeneous medium

Continuous-time random walks (CTRWs) are an elementary model for particle motion subject to randomized waiting times. In this paper, we consider the case where the distribution of waiting times depends on the location of the particle. In particular, we analyze the case where the medium exhibits a bounded trapping region in which the particle is subject to CTRW with power-law waiting times and regular diffusion elsewhere. We derive a diffusion limit for this inhomogeneous CTRW. We show that depending on the index of the power-law distribution, we can observe either nonlinear subdiffusive or standard diffusive motion.