More Uses of Exchangeability: Representations of Complex Random Structures

TL;DR

This paper reviews the broad applications of exchangeability in representing complex random structures across various fields like graph theory, combinatorics, and stochastic processes, highlighting both classical and recent developments.

Contribution

It provides a comprehensive overview of exchangeability's role in representing complex random structures, including new insights into their diverse applications.

Findings

Unified framework for exchangeable representations

Connections between exchangeability and complex structures

Illustrations across multiple domains

Abstract

We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum random trees; second-order limits of distances in random graphs; isometry classes of metric spaces with probability measures; limits of dense random graphs; and more sophisticated uses in finitary combinatorics.