Random Walks in a One-Dimensional Lévy Random Environment

  title={Random Walks in a One-Dimensional L{\'e}vy Random Environment},
  author={A. Bianchi and G. Cristadoro and M. Lenci and Marilena Ligab{\`o}},
  journal={Journal of Statistical Physics},
We consider a generalization of a one-dimensional stochastic process known in the physical literature as Lévy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random… Expand
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  • Barkai, Fleurov, Klafter
  • Mathematics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 2000
A Levy-Lorentz gas in which a light particle is scattered by static point scatterers arranged on a line is introduced and it is shown that under certain conditions the mean square displacement of the particle obeys <x(2)(t)>>/=Ct3-gamma for 1<gamma<2. Expand
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