The upper tail problem for subgraph counts in the Erdos-Renyi graph, introduced by Janson-Ruciński, has attracted a lot of attention. There is a class of Gibbs measures associated with subgraph counts, called exponential random graph model (ERGM). Despite its importance, lots of fundamental questions have remained unanswered owing to the lack of exact solvability. In this talk, I will talk about a brief overview on the upper tail problem and the concentration of measure results for the ERGM. Joint work with Shirshendu Ganguly and Ella Hiesmayr.
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