Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

Author(s)

Borges, G. M. ^[1] ; Ferreira, A. S. ^[2] ; da Silva, M. A. A. ^[3] ; Cressoni, J. C. ^{[3, 4]} ; Viswanathan, G. M. ^{[1, 4]} ; Mariz, A. M. ^[1]

Affiliation

^[1] Univ Fed Rio Grande do Norte, Dept Fis Teor & Expt, BR-59078900 Natal, RN - Brazil

^[2] Univ Fed Pernambuco, Dept Fis, BR-50670901 Recife, PE - Brazil

^[3] Univ Sao Paulo, FCFRP, Dept Quim & Fis, BR-14040903 Ribeirao Preto, SP - Brazil

^[4] Univ Fed Alagoas, Inst Fis, BR-57072970 Maceio, AL - Brazil

• Document type: Journal article
• Source: European Physical Journal B; v. 85, n. 9 SEP 2012.
• Web of Science Citations: 9

Abstract

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e. g., fractional Brownian motion, Levy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always ``remember{''} the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation sigma t which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile. (AU)

• FAPESP's process: 11/06757-0 - Diffusive processes: random walkers with memory
• Grantee: Marco Antonio Alves da Silva
• Support Opportunities: Regular Research Grants
• FAPESP's process: 11/13685-6 - Analytical and computational modelling of diffusive systems
• Grantee: Marco Antonio Alves da Silva
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil