A random walk model with a mixed memory profile: Exponential and rectangular profile

Author(s)

de Lacerda, K. J. C. C. ; da Silva, L. R. ; Viswanathan, G. M. ; Cressoni, J. C. ; da Silva, M. A. A.

• Document type: Journal article
• Source: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 597, p. 6-pg., 2022-04-08.

Abstract

The theory of Markovian random walks is consolidated and very well understood, however the theory of non-Markovian random walks presents many challenges due to its remarkably rich phenomenology. An important open problem in this context is to study how the diffusive properties of random walk processes change when memoryinduced correlations are introduced. In this work we propose a model of a random walk that evolves in time according to past memories selected from rectangular (flat) and exponentially decaying memory profiles. In this mixed memory profile model, the walker remembers either the last B steps with equal a priori probability or the steps A prior to B with exponentially decaying probability, for a total number of steps equal to A + B. The diffusive behavior of the walk is numerically examined through the Hurst exponent (H). Even in the lack of exact solutions, we are still able to show that the model can be mapped onto a RW model with rectangular memory profile. (c) 2022 Elsevier B.V. All rights reserved. (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