Before revision:  Due to the random graphs approach these results bear a considerable robustness to local uncertainties and small changes of the network structure over time. In particular, it is possible to condense the precise micro-structure of the network to macroscopic statistics. Applications of our theory demonstrate that indeed the features captured by our model can have significant impact on system stability;
After revision:  This is the first instance that default contagion is rigorously studied in a model outside the class of rank one models and several technical challenges arise. Moreover, in contrast to previous work, in which networks could be classified as resilient or non resilient, independent of the distribution of the shock, information about the shock becomes important in our model and a more refined resilience condition arises. Among other applications of our theory demonstrate that indeed the features captured by our model can have significant impact on system stability;