Non-Gaussian propagator for elephant random walks

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]

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

• 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