Functional equation for the crossover in the model of one-dimensional Weierstrass random walks

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. © 2016, Pleiades Publishing, Ltd.

Authors
Rudoi Y.G. 1 , Kotel’nikova O.A.2
Editors
-
Publisher
-
Number of issue
3
Language
English
Pages
1818-1823
Status
Published
Department
-
Number
-
Volume
189
Year
2016
Organizations
  • 1 Peoples’ Friendship University of Russia, Moscow, Russian Federation
  • 2 Lomonosov Moscow State University, Moscow, Russian Federation
Keywords
anomalous diffusion; fractal dimension; functional pressure; Markov process; normal diffusion; Weierstrass function
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/3721/