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Fractal random walks |
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| Authors: | B. D. Hughes E. W. Montroll M. F. Shlesinger |
| Affiliation: | (1) Department of Chemical Engineering and Materials Science, University of Minnesota, 55455 Minneapolis, Minnesota;(2) Institute for Physical Science and Technology, University of Maryland, 20742 College Park, Maryland;(3) La Jolla Institute, USA |
| Abstract: | We consider a class of random walks (on lattices and in continuous spaces) having infinite mean-squared displacement per step. The probability distribution functions considered generate fractal self-similar trajectories. The characteristic functions (structure functions) of the walks are nonanalytic functions and satisfy scaling equations.Supported by the Commonwealth Scientific and Industrial Research Organization (Australia).Supported by the Xerox Corporation.Supported in part by a grant from DARPA. |
| Keywords: | random walks stochastic processes fractals scaling stable distributions nondifferentiable functions |
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