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.
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Supported by the Commonwealth Scientific and Industrial Research Organization (Australia).
Supported by the Xerox Corporation.
Supported in part by a grant from DARPA.
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Hughes, B.D., Montroll, E.W. & Shlesinger, M.F. Fractal random walks. J Stat Phys 28, 111–126 (1982). https://doi.org/10.1007/BF01011626
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DOI: https://doi.org/10.1007/BF01011626