  Urban outputs often scale superlinearly with city population. A difficulty in
understanding the mechanism of this phenomenon is that different outputs differ
considerably in their scaling behaviors. Here, we formulate a physics-based
model for the origin of superlinear scaling in urban outputs by treating human
interaction as a random process. Our model suggests that the increased
likelihood of finding required collaborations in a larger population can
explain this superlinear scaling, which our model predicts to be non-power-law.
Moreover, the extent of superlinearity should be greater for activities that
require more collaborators. We test this model using a novel dataset for seven
crime types and find strong support.
