On the Ensemble Average of Generalized Truncated Random Walk

Abstract

A new analytical solution is developed for the one-and two-dimensional generalized discrete time random walk with discrete and finite length of jumping. It is shown that the ensemble average of the mean square displacement has a linear relation with time. This result is general and independent of mathematical form of distribution function but magnitude of diffusion coefficient depends on the distribution function. This result confirms our previous numerical work. The truncated Levy flight is studied as a special case and the diffusion coefficient for different maximum length of jump is calculated numerically. The obtained results are in good agreement with the analytical solution.