Anomalous diffusion in correlated continuous time random walks

Abstract

We demonstrate that continuous time random walks in which successive waiting\ntimes are correlated by Gaussian statistics lead to anomalous diffusion with\nmean squared displacement <r^2(t)>~t^{2/3}. Long-ranged correlations of the\nwaiting times with power-law exponent alpha (0<alpha<=2) give rise to\nsubdiffusion of the form <r^2(t)>~t^{alpha/(1+alpha)}. In contrast correlations\nin the jump lengths are shown to produce superdiffusion. We show that in both\ncases weak ergodicity breaking occurs. Our results are in excellent agreement\nwith simulations.\n