Non-Levy stable random walk propagators for a non-Markovian walk with both superdiffusive and subdiffusive regimes

Author(s)

da Silva, M. A. A. ; Rocha, E. C. ; Cressoni, J. C. ; da Silva, L. R. ; Viswanathan, G. M.

• Document type: Journal article
• Source: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 538, p. 5-pg., 2020-01-15.

Abstract

One of the most important quantities of interest in the theory of diffusion and transport is the random walk propagator. For Markovian processes, such as the standard Brownian random walk and Levy flights, the functional form of the random walk propagator is well understood. Similarly, for certain kinds of simple non-Markovian processes, such as Levy walks, the problem can be mapped to a solvable Markovian model. However, more complicated non-Markovian walks pose a challenge. Here we study a non-Markovian model that is rich enough to exhibit superdiffusion, normal diffusion and subdiffusion regimes (Kumar, Harbola, and Lindenberg (2010)). We numerically estimate propagators for this model and obtain good fits with a family of non-Levy propagators based on the Tsallis q-exponential function. We conclude that stops and restrictions play similar roles in the long time limit of the propagator. (C) 2019 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 16/03918-7 - Characterization and memory effects in stochastic processes
• Grantee: Marco Antonio Alves da Silva
• Support Opportunities: Regular Research Grants
• FAPESP's process: 17/01176-6 - Memory effects and characterization in stochastic processes
• Grantee: Marco Antonio Alves da Silva
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil