We consider an idealized stochastic model for a network of pulse-coupled
oscillators where there is randomness both in input and in network
architecture.  We describe the various types of dynamics which arise in 
this system, analyze scalings which arise in certain limits, and study the 
various "finite-size" effects as perturbations of these limits.  Most 
notably, for certain parameters this network supports both synchronous and 
asynchronous modes of behavior and will switch stochastically between these 
modes due to "rare events".   We also relate the analysis of certain scaling 
limits of this network to classical results involving the size of components 
in the Erdos-Renyi random graph.  This work is joint with Charles Peskin and 
Joel Spencer.