Lectures

Second focus week of the Workshop on Graphs and Randomness. Minicourse on “Complex graphs and networks” by Remco van den Hofstad (TU Eindhoven). Invited participants: Béla Bollobás (Cambridge), Remco van der Hofstad (TU Eindhoven), Yuval Peres (Microsoft Research), Joel Spencer (Courant Inst, NYU). The systematic study of Random Graphs started with the seminal of Erdos and Rényi in the 1960’s. Most early work on the topic came from the combinatorics community. Probabilists gradually joined in, bringing sophisticated tools that shed new light on the topic. At the same time, discrete mathematics enriched probability with new problems, techniques and ideas. Further stimulus came from “complex networks” that appear in many application domains. A different, but related direction is the study of random processes on graphs. Random walks on finite graphs, and their properties such as mixing, hitting and cover times, are a classical topic. New discoveries in this area are still being made, and many combinatorialists have made significant contributions. Interacting particle systems on finite graphs have recently become prominent, partly because of their usefulness as models for many phenomena.This focus week brings together leading experts in the above topics. We will have a minicourse and a small number of talks meant to encourage further research.