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

• Published in: Physica A 2022-07, Vol.597, p.127301, Article 127301
• Main Authors: de Lacerda, K.J.C.C., da Silva, L.R., Viswanathan, G.M., Cressoni, J.C., da Silva, M.A.A.
• Format: Article
• Language: English
• Subjects: Anomalous diffusion; Memory correlations; Non-Markovian; Random processes; Random walk
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2022.127301

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 memory-induced 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. •The RW evolves in time according to two memory profiles.•The two-fold decision process is inspired by certain biological memory processes.•The model presents an interesting approach to deal with non-Markovian models.•The Hurst exponent values show transition from normal to superdiffusion.