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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This research was supported by the Ministry of Education and Science of the Russian Federation, Russian Academic Excellence Program for the Peoples’ Friendship University of Russia, 2016-2020.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 189, No. 3, pp. 477–484, December, 2016.
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Rudoi, Y.G., Kotel’nikova, O.A. Functional equation for the crossover in the model of one-dimensional Weierstrass random walks. Theor Math Phys 189, 1818–1823 (2016). https://doi.org/10.1134/S0040577916120138
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DOI: https://doi.org/10.1134/S0040577916120138