Exact Results for the Nonergodicity of d-Dimensional Generalized Lévy Walks.

We provide analytical results for the ensemble-averaged and time-averaged squared displacement, and the randomness of the latter, in the full two-dimensional parameter space of the d-dimensional generalized Lévy walk introduced by Shlesinger et al. [Phys. Rev. Lett. 58, 1100 (1987)PRLTAO0031-900710.1103/PhysRevLett.58.1100]. In certain regions of the parameter plane, we obtain surprising results such as the divergence of the mean-squared displacements, the divergence of the ergodicity breaking parameter despite a finite mean-squared displacement, and subdiffusion which appears superdiffusive when one only considers time averages.