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Published on: March 27, 2015
Non-Gaussian propagator for elephant random walks
M A A da Silva1, J C Cressoni, Gunter M Schütz
1Departamento de Física e Química, FCFRP, Universidade de São Paulo, 14040-903 Ribeirão Preto, SP, Brazil.
Abstract:
For almost a decade the consensus has held that the random walk propagator for the elephant random walk (ERW) model is a Gaussian. Here we present strong numerical evidence that the propagator is, in general, non-Gaussian and, in fact, non-Lévy. Motivated by this surprising finding, we seek a second, non-Gaussian solution to the associated Fokker-Planck equation. We prove mathematically, by calculating the skewness, that the ERW Fokker-Planck equation has a non-Gaussian propagator for the superdiffusive regime. Finally, we discuss some unusual aspects of the propagator in the context of higher order terms needed in the Fokker-Planck equation.
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