Stroboscopic observation of a random walker

Authors

  • R. Mansilla Universidad Nacional Autónoma de México

DOI:

https://doi.org/10.31349/SuplRevMexFis.1.4.54

Keywords:

mobile agentes, gaussian random walker

Abstract

The patterns of motion of mobile agents have received recently wide attention in the literature. There is a number of recent studies centered around the motion behavior of many agents ranging from albatrosses to human beings. Special attention has been given to the covered distances statistical distributions. In some cases, due to the lack of accurate data about the motion of the agents it has been necessary to plan very clever experiments to obtain them.  These experiments try to infer the statistical properties of the agents' real motion from the observed positions in consecutive time intervals.  The length of the time intervals are random variables taking their values from a previously known statistical distribution or from a distribution deduced from empirical data. The aim of this work is to demonstrate that for a Gaussian Random Walker it is, in general, impossible to recover the real motion patterns distribution from the stroboscopic observation of the agents unless the length of the intervals between two consecutive measurements are equal. Moreover, it is also shown that the distances distribution strongly depends on the agents' observation time intervals. These claims are sustained by numerical experiments.

Author Biography

R. Mansilla, Universidad Nacional Autónoma de México

Researcher at Center for Interdisciplinary Reseach in Science and the Humanities

References

Viswanathan G M, Afanasyev V, Buldyrev S V, Murphy E J, Prince P A et al. (1996) Levy flight search patterns of wandering albatrosses. Nature, 381: 413-415.

Edwards A M, Phillips R A, Watkins N W, Freeman M P, Murphy E J et al. (2007) Revisiting Levy type search patterns of wandering albatrosses, bumblebees and deer. Nature 449: 1044-1048.

Nagy M, Ákos Z, Biro D, Vicsek T (2010) Hierarchical group dynamics in pigeon flocks. Nature 464: 890-893.

Ramos-Fernandez G, Mateos J L, Miramontes O, Cocho G, Larralde H et al. (2004) Levy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi). Behavioral Ecology and Sociobiology 55: 223-230.

Atkinson R P, Rhodes C J, Macdonald D W, Anderson R M (2002) Scale-free dynamics in the movement patterns of jackals. OIKOS 98: 134-140.

Brockmann D, Hufnagel L, Geisel T (2006) Scaling law of human travels. Nature 439: 462-465.

González M C, Hidalgo C A, Barabási A-L, (2008) Understanding individual human mobility patterns. Nature 453: 779-782.

Candia J, Gonzalez M C, Wang P, Schoenharl T, Madey G et al (2008) Uncovering individual and collective human dynamics from mobile phone records. Journal of Physics A: Mathematical and Theoretical, 41: 1-11.

Song Ch, Koren T, Wang P, Barabasi A-L (2010) Modeling the scaling properties of human mobility. Nature Physics 6: 818-823.

S. Benhamou (2007) How many animals really do the Levy walks. Ecology 88: 1962-1969.

Downloads

Published

2020-10-07

How to Cite

1.
Mansilla R. Stroboscopic observation of a random walker. Supl. Rev. Mex. Fis. [Internet]. 2020 Oct. 7 [cited 2024 Mar. 28];1(4):54-8. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/5272