Functional equation for the crossover in the model of one-dimensional Weierstrass random walks |
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| Authors: | Yu. G. Rudoi O. A. Kotel’nikova |
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| Affiliation: | 1.Peoples’ Friendship University of Russia,Moscow,Russia;2.Lomonosov Moscow State University,Moscow,Russia |
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| Abstract: | We consider the problem of one-dimensional symmetric diffusion in the framework of Markov random walks of the Weierstrass type using two-parameter scaling for the transition probability. We construct a solution for the characteristic Lyapunov function as a sum of regular (homogeneous) and singular (nonhomogeneous) solutions and find the conditions for the crossover from normal to anomalous diffusion. |
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