  We study the effects of correlations in a random environment on a random
walker. The dependence of its asymptotic speed on the correlations is a
nonperturbative effect as it is not captured by a homogeneous version of the
same environment. For a slowly cooling environment, the buildup of correlations
modifies the walker's speed and, by so, realizes acceleration. We remark on the
possible relevance in the discussion of cosmic acceleration as traditionally
started from the Friedmann equations, which, from a statistical mechanical
point of view, would amount to a mean-field approximation. Our environment is
much simpler though, with transition rates sampled from the one-dimensional
Ising model and allowing exact results and detailed velocity characteristics.
