Abstract:

Lovász and a number of coworkers have constructed a theory of graph limits for dense graphs. I will show how this theory is connected to random infinite graphs, and through them to the theory of exchangeable random arrays by Aldous, Hoover and Kallenberg. I will also show how the theory has versions for other similar combinatorial structures, such as directed graphs and partially ordered sets. (This is mainly based on joint work with Persi Diaconis.)