Random Walks on Attractive Spin-Flip Dynamics: Law of Large Numbers and Large Deviation Estimates

Stein Andreas Bethuelsen, Markus Heydenreich

Published 2014-11-13Version 1

We consider random walks in dynamic random environment on Z^d, d \geq 1, where the dynamics are given by interacting particle systems of 2-state type. Our main result is a general law of large numbers for the walker when the environment is attractive and started from all sites equal to the same state. The proof also yields information about the large deviation behavior of the walker. As prime example we study the random walk on the contact process, for which we obtain a law of large numbers in arbitrary dimension. For this model, further properties about the speed are derived.