The mean number of distinct sites visited by an elephant random walker in one-dimension

  • Bimbo Alexis Bacones Galit National Institute of Physics, University of the Philippines Diliman
  • Jose Perico Henson Esguerra National Institute of Physics, University of the Philippines Diliman http://orcid.org/0000-0002-9977-0632

Abstract

Schütz and Trimper in 2004 introduced a non-Markovian random walk that involved a random walker that has access to the complete history of what it has done in the past and uses this knowledge to influence its future motion. Today, this random walk is known as the elephant random walk. In this work, we have analyzed the mean number of distinct sites visited by an elephant random walker in one-dimension, numerically. It was found that varying the value of the initial step parameter q did not affect the mean number of distinct sites visited by an elephant random walker. It was also found that high values of the memory parameter, p, causes the elephant random walker to visit more sites per time step specially in the superdiffusive case of the elephant random walk, i.e. p ≥ 3/4 , where the rate of increase in the mean number of distinct sites visited per time step is more drastic as opposed to the rates for the normal diffusive elephant random walkers.

Published
2017-05-09
How to Cite
[1]
B. A. Galit and J. P. Esguerra. The mean number of distinct sites visited by an elephant random walker in one-dimension, Proceedings of the Samahang Pisika ng Pilipinas 35, SPP-2017-PB-01 (2017). URL: https://paperview.spp-online.org/proceedings/article/view/120.
Section
Poster Session B (Complex Systems, Simulations, and Theoretical Physics)