de Finetti Style Theorems With Applications to Network Analysis

TL;DR

This paper extends de Finetti's Theorem to new cases and demonstrates its application in analyzing random networks, providing a comprehensive and accessible overview of the theory and its practical implications.

Contribution

It introduces a new decomposition theorem for cases not previously covered and applies it innovatively to network analysis.

Findings

New decomposition theorem for non-traditional cases

Application of de Finetti's Theorem to network analysis

Accessible exposition for broader readership

Abstract

A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti's Theorem. In its original form it applies to infinite 0-1 valued exchangeable sequences. Later it was extended and generalized in numerous directions. After reviewing this line of development, we present our new decomposition theorem, covering cases that have not been previously considered. We also introduce a novel way of applying these types of results in the analysis of random networks. For self-containment, we provide the introductory exposition in more details than usual, with the intent of making it also accessible to readers who may not be closely familiar with the subject.