(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Blondel, Oriane; Hilário, Marcelo R.; Santos, Renato Soares dos; Sidoravicius, Vladas; Teixeira, Augusto
We study the evolution of a random walker on a conservative dynamic
random environment composed of independent particles performing simple
symmetric random walks, generalizing results of [16] to higher dimensions and
more general transition kernels without the assumption of uniform ellipticity
or nearest-neighbour jumps. Specifically, we obtain a strong law of large
numbers, a functional central limit theorem and large deviation estimates for
the position of the random walker under the annealed law in a high density
regime. The main obstacle is the intrinsic lack of monotonicity in
higher-dimensional, non-nearest neighbour settings. Here we develop more
general renormalization and renewal schemes that allow us to overcome this
issue. As a second application of our methods, we provide an alternative
proof of the ballistic behaviour of the front of (the discrete-time version
of) the infection model introduced in [23].
