Large deviation principle for empirical measures of multitype random networks

Abstract

In this article, we study the stochastic block model also known as the multi-type random networks (MRNs). For the stochastic block model or the MRNs, we define the empirical group measure, empirical cooperative measure and the empirical locality measure. We prove joint large deviation principles for these empirical measures of the stochastic block model in the weak topology. These results will form the basis of understanding the asymptotics of the evolutionary and co-evolutionary processes on the stochastic block model.