POISSON APPROXIMATION FOR SUBGRAPH COUNTS IN A GRAPHEX MODEL

Abstract

In this thesis, we begin with an overview of the Stein-Chen method and the graphex random graph model, followed by a survey of past work related to the application of the Stein-Chen method to approximate subgraph counts in random graphs. We then consider the problem of approximating the distribution of subgraph counts in a random graph generated by a graphex process. The Stein-Chen method is used to derive a Poisson approximation for the number of subgraphs of a random graph generated by a graphex process isomorphic to a fixed graph.