(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Blondel, Oriane; Hilário, Marcelo R.; Santos, Renato dos; Sidoravicius, Vladas; Teixeira, Augusto
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.
