Exchangeability and large Random networks

Specialeforsvar ved Frederik Sørensen

Titel: Exchangeability and large Random Networks

Abstract: In this thesis we will rigorously develop the theory needed to characterize exchangeable random arrays. Initially we will cover results on conditional independence, then we will discuss exchangeability for sequences and then develop several results regarding exchangeable random arrays, culminating with the proof of the Aldous-Hoover Representation Theorem. We generalize graphs to graphons and show that we can find a metric usefull for concluding graph convergence. The space of graphons is compact in this metric, and it identifies the weakly isomorphic graphons. Furthermore, we show that the limit of any convergent graph sequence is a graphon. Extending this theory to random graphs, we shall construct a link between exchangeable random graphs and limits of convergent graph sequences, showing that there is a bijective correspondence between the two. 

Vejleder: Steffen Lauritzen
Censor:   Alexander Sokol, Nordea