Abstract
Curves of asymptotic probability densities appropriate to the continuous time random walk model of Montroll and Weiss are presented and are calculated numerically using the fast Fourier transform. The behavior of the moments is briefly discussed and it is shown that the Einstein formula relating the diffusion and mobility coefficients can be generalized to include the case where the mean waiting time between hops is infinite.
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References
J. K. E. Tunaley, Asymptotic Solutions of the Continuous Time Random Walk Model of Diffusion,J. Stat. Phys. (1974), in press.
E. W. Montroll and G. H. Weiss,J. Math. Phys. 6:167 (1965).
W. Feller,An Introduction to Probability Theory and its Applications, Vol. 2, 2nd ed., Wiley, New York (1971).
E. W. Montroll and H. Sher,J. Stat. Phys. 9:101 (1973).
M. F. Shlesinger, Asymptotic Solutions of Continuous Time Random Walks,J. Stat. Phys. 10:421 (1974).
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Tunaley, J.K.E. Some properties of the asymptotic solutions of the Montroll-Weiss equation. J Stat Phys 12, 1–10 (1975). https://doi.org/10.1007/BF01024180
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DOI: https://doi.org/10.1007/BF01024180