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