We study the dynamics of information (or virus) dissemination by $m$ mobile
agents performing independent random walks on an $n$-node grid. We formulate
our results in terms of two scenarios: broadcasting and gossiping. In the
broadcasting scenario, the mobile agents are initially placed uniformly at
random among the grid nodes. At time 0, one agent is informed of a rumor and
starts a random walk. When an informed agent meets an uninformed agent, the
latter becomes informed and starts a new random walk.