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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Non-Gaussian propagator for elephant random walks

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Author(s):
da Silva, M. A. A. [1] ; Cressoni, J. C. [1, 2] ; Schuetz, Gunter M. [3] ; Viswanathan, G. M. [2, 4] ; Trimper, Steffen [5]
Total Authors: 5
Affiliation:
[1] Univ Sao Paulo, FCFRP, Dept Quim & Fis, BR-14040903 Ribeirao Preto, SP - Brazil
[2] Univ Fed Alagoas, Inst Fis, BR-57072970 Maceio, AL - Brazil
[3] Forschungszentrum Julich, Inst Complex Syst 2, D-52428 Julich - Germany
[4] Univ Fed Rio Grande do Norte, Dept Fis Teor & Expt, BR-59078900 Natal, RN - Brazil
[5] Univ Halle Wittenberg, Inst Phys, D-06099 Halle - Germany
Total Affiliations: 5
Document type: Journal article
Source: Physical Review E; v. 88, n. 2 AUG 9 2013.
Web of Science Citations: 18
Abstract

For almost a decade the consensus has held that the random walk propagator for the elephant random walk (ERW) model is a Gaussian. Here we present strong numerical evidence that the propagator is, in general, non-Gaussian and, in fact, non-Levy. Motivated by this surprising finding, we seek a second, non-Gaussian solution to the associated Fokker-Planck equation. We prove mathematically, by calculating the skewness, that the ERW Fokker-Planck equation has a non-Gaussian propagator for the superdiffusive regime. Finally, we discuss some unusual aspects of the propagator in the context of higher order terms needed in the Fokker-Planck equation. (AU)

FAPESP's process: 11/06757-0 - Diffusive processes: random walkers with memory
Grantee:Marco Antonio Alves da Silva
Support type: Regular Research Grants
FAPESP's process: 11/21089-4 - Large deviation properties of the ASEP with random rates
Grantee:Serguei Popov
Support type: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 11/13685-6 - Analytical and computational modelling of diffusive systems
Grantee:Marco Antonio Alves da Silva
Support type: Research Grants - Visiting Researcher Grant - Brazil