title: Distributional ergodicity in stored-energy-driven Lévy flights.
abstract: We study a class of random walk, the stored-energy-driven Lévy flight (SEDLF), whose jump length is determined by a stored energy during a trapped state. The SEDLF is a continuous-time random walk with jump lengths being coupled with the trapping times. It is analytically shown that the ensemble-averaged mean-square displacements exhibit subdiffusion as well as superdiffusion, depending on the coupling parameter. We find that time-averaged mean-square displacements increase linearly with time and the diffusion coefficients are intrinsically random, a manifestation of distributional ergodicity. The diffusion coefficient shows aging in subdiffusive regime, whereas it increases with the measurement time in superdiffusive regime.
authors.affiliation: Department of Mechanical Engineering, Keio University, Yokohama, 223-8522, Japan. akimoto@z8.keio.jp
authors.forename: Takuma
authors.initials: T
authors.lastname: Akimoto
authors.forename: Tomoshige
authors.initials: T
authors.lastname: Miyaguchi