Large deviation principles for empirical measures of the multitype random networks

TL;DR

This paper establishes large deviation principles for empirical measures in multitype random networks, providing foundational insights into their asymptotic behavior and aiding the understanding of evolutionary processes on such networks.

Contribution

It derives large deviation principles for key empirical measures in multitype random networks, a novel theoretical contribution to network probability analysis.

Findings

Large deviation principles for empirical group, cooperative, and locality measures.

Framework for analyzing asymptotics of evolutionary processes on multitype networks.

Foundation for future studies on stochastic block models and their dynamics.

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 derive large deviation principles for the empirical measures in the weak topology. These results will form the basis of understanding asymptotics of the evolutionary and co-evolutionary processes on the stochastic block model.