Random walks on finite high-dimensional cubic lattices with a single trap

Exact numerical results are reported for the problem of unbiased, nearest-neighbor random walks on small, finite d ( > 3)-dimensional Cartesian lattices with a single trap. The (slight) dependence of the survival probability on system dimensionality above d = 3 is compared with the predictions of...

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Bibliographic Details
Published in:Chemical physics letters 1985-01, Vol.120 (4), p.388-392
Main Authors: Politowicz, Philip A., Kozak, John J., Weiss, George H.
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Nonlinear dynamics and nonlinear dynamical systems
Other techniques and industries
Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
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Summary:Exact numerical results are reported for the problem of unbiased, nearest-neighbor random walks on small, finite d ( > 3)-dimensional Cartesian lattices with a single trap. The (slight) dependence of the survival probability on system dimensionality above d = 3 is compared with the predictions of random walk theory, with the latter in excellent agreement with the data. Calculation of the relative width, skewness and kurtosis of the underlying (continuous) probability distribution function for the problem confirms that the process may be accurately described by an exponential distribution function, as was predicted recently by Weiss, Havlin and Bunde. Attention is drawn to the relative speed at which the calculated survival time distribution reaches the theoretically expected exponential form.
ISSN:0009-2614
1873-4448
DOI:10.1016/0009-2614(85)85625-6