Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 43, Issue 8, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/43/8/082002
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We demonstrate that continuous time randomwalks inwhich successivewaiting times are correlated by Gaussian statistics lead to anomalous diffusion with the mean squared displacement < r(2)(t) similar or equal to t(2/3). Long-ranged correlations of the waiting times with a power-law exponent alpha (0 < alpha <= 2) give rise to subdiffusion of the form < r(2)(t) similar or equal to t(alpha/(1+alpha)). In contrast, correlations in the jump lengths are shown to produce superdiffusion. We show that in both cases weak ergodicity breaking occurs. Our results are in excellent agreement with simulations.
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