  Consider a stochastic growth model on $\mathbb{Z} ^d$. Start with some active
particle at the origin and sleeping particles elsewhere. The initial number of
particles at $x \in \mathbb{Z} ^d$ is $\eta(x)$, where $\eta (x)$ are
independent random variables distributed according to $\mu$. Active particles
perform a simple continuous-time random walk while sleeping particles stay put
until the first arrival of an active particle to their location. Upon the
arrival all sleeping particles at the site activate at once and start moving
according to their own simple random walks. The aim of this paper is to give
conditions on $\mu$ under which the spread of the process is linear or faster
than linear. The proofs rely on comparison to various percolation models.
