WIAS Preprint No. 2434, (2017)

Random walk on random walks: Low densities


  • Blondel, Oriane
  • Hilário, Marcelo R.
  • Soares dos Santos, Renato
  • Sidoravicius, Vladas
  • Teixeira, Augusto

2010 Mathematics Subject Classification

  • 60F15 60K35 82B41 82C22 82C44


  • Random walk, dynamic random environment, law of large numbers, central limit theorem, large deviations, renormalization, regeneration




We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on particles. Surprisingly, the random walker may behave very differently depending on whether the underlying environment particles perform lazy or non-lazy random walks, which is related to a notion of permeability of the system. We also provide a strong law of large numbers, a functional central limit theorem and large deviation bounds under an ellipticity condition.

Appeared in

  • Ann. Appl. Probab., 30:4 (2020), pp. 1614-1641.

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