Stretched-Gaussian asymptotics of the truncated Lévy flights for the diffusion in nonhomogeneous media

Details Stretched-Gaussian asymptotics of the truncated Lévy flights for the diffusion in nonhomogeneous media Stretched-Gaussian asymptotics of the truncated Lévy flights for the diffusion in nonhomogeneous media

2009-06-09

arxiv.org/abs/0906.1706v1

Physica A 388 (2009) 1057

Physics

Condensed Matter

Statistical Mechanics

19 pages, 5 figures

Scientific paper

10.1016/j.physa.2008.12.059

The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable diffusion coefficient, is solved in the diffusion limit. That solution resolves itself to the stretched Gaussian when the order parameter $\mu\to2$. The truncation of the L\'evy flights, in the exponential and power-law form, is introduced and the corresponding random walk process is simulated by the Monte Carlo method. The stretched Gaussian tails are found in both cases. The time which is needed to reach the limiting distribution strongly depends on the jumping rate parameter. When the cutoff function falls slowly, the tail of the distribution appears to be algebraic.

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