A stochastic model of randomly accelerated walkers for human mobility

Riccardo Gallotti (1) , Armando Bazzani (2) , Sandro Rambaldi (2) , Marc Barthelemy (3, 1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 INFN, Sezione di Bologna - Istituto Nazionale di Fisica Nucleare, Sezione di Bologna
3 CAMS - Centre d'Analyse et de Mathématique sociales

The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations [6]. We illustrate this in the case of human mobility [1-3] and foraging human patterns [4] where empirical long-tailed distributions of jump sizes have been associated to scale-free super-diffusive random walks called L\'evy flights [5]. Here, we introduce a new class of accelerated random walks where the velocity changes due to acceleration kicks at random times, which combined with a peaked distribution of travel times [7], displays a jump length distribution that could easily be misinterpreted as a truncated power law, but that is not governed by large fluctuations. This stochastic model allows us to explain empirical observations about the movements of 780,000 private vehicles in Italy, and more generally, to get a deeper quantitative understanding of human mobility.

Keywords: Physics and Society (physics.soc-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)

Domains: Physics [physics]; Physics [physics]; Physics and Society [physics.soc-ph]

Riccardo Gallotti, Armando Bazzani, Sandro Rambaldi, Marc Barthelemy. A stochastic model of randomly accelerated walkers for human mobility. Nature Communications, 2016, 7, pp.12600. ⟨10.1038/ncomms12600⟩. ⟨cea-01334194⟩