On Watts cascade model with random link weights

We study an extension of D. Watts 2002 model of information cascades in social networks where edge weights are taken to be random, an innovation motivated by recent applications of cascade analysis to sys-temic risk in financial networks. The main result is a probabilistic analysis that characterizes the cascade in an in?nite network as the ?xed point of a vector-valued mapping, explicit in terms of convolution inte-grals that can be ef?ciently evaluated numerically using the fast Fourier transform algorithm. A second result gives an approximate probabilistic analysis of cascades on "real world networks", finite networks based on a ?xed deterministic graph. Extensive cross testing with Monte Carlo estimates shows that this approximate analysis performs surprisingly well, and provides a fiexible "microscope" that can be used to investigate properties of information cascades in real world networks over a wide range of model parameters.