social networks are often represented by directed graphs where the nodes are individuals and the edges indicate a form of social relationship. a simple way to model the diffusion of ideas, innovative behavior, or word-of-mouth effects on such a graph is to consider a stochastic process of ``infection'': each node becomes infected once an activation function of the set of its infected neighbors crosses a random threshold value. i will prove a conjecture of kempe, kleinberg, and tardos which roughly states that if such a process is ``locally'' submodular then it must be ``globally'' submodular on average. the significance of this result is that it leads to a good algorithmic solution to the problem of maximizing the spread of influence in the network--a problem known in data mining as "viral marketing"'. this is joint work with elchanan mossel.