We prove a shape theorem for a growing set of simple
random walks on Z^d, known as frog model. The dynamics of
this process is described as follows: There are active particles,
which perform independent discrete time SRWs, and sleeping
particles, which do not move. When a sleeping particle is hit by
an active particle, the former becomes active as well.
Initially, a random number of particles is placed into each site.
At time 0 all particles are sleeping, except for those
placed at the origin. We prove that the set of all sites
visited by active particles, rescaled by the elapsed time,
converges to a compact convex set.
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