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

Autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 597, p. 6-pg., 2022-04-08.

Resumo

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)

• Processo FAPESP: 11/06757-0 - Processos difusivos: caminhantes aleatórios com memória
• Beneficiário: Marco Antonio Alves da Silva
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 11/13685-6 - Modelagem analítica e computacional de sistemas difusivos
• Beneficiário: Marco Antonio Alves da Silva
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil