Random walk on random walks: low densities

Oriane Blondel (1, 2, 3) , Marcelo R Hilário , Renato S dos Santos , Vladas Sidoravicius (4) , Augusto Teixeira

1 ICJ - Institut Camille Jordan
2 CNRS - Centre National de la Recherche Scientifique
3 PSPM - Probabilités, statistique, physique mathématique
4 IMPA Jean-Christophe Yoccoz

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.

Domaines: Probabilités [math.PR]

Oriane Blondel, Marcelo R Hilário, Renato S dos Santos, Vladas Sidoravicius, Augusto Teixeira. Random walk on random walks: low densities. The Annals of Applied Probability, 2020, 30 (4), pp.1614-1641. ⟨10.1214/19-AAP1537⟩. ⟨hal-01616296⟩