Concentration of measure phenomenon in sub-critical exponential random graphs

Seminar: Probability Seminar | October 16 | 3:10-4 p.m. | 1011 Evans Hall

 Kyeongsik Nam, U.C. Berkeley Mathematics

 Department of Statistics

The exponential random graph model (ERGM) is a central object in the study of clustering properties in social networks as well as canonical ensembles in statistical physics. It is a version of the well known Erd˝os-R´enyi graphs, obtained by tilting according to the subgraph counting Hamiltonian. Despite its importance in the theory of random graphs, lots of fundamental questions have remained unanswered owing to the lack of exact solvability. In this talk, I will introduce a series of new concentration of measure results for the ERGM throughout the entire sub-critical phase, including a Poincaré inequality, Gaussian concentration, and a central limit theorem. Joint work with Shirshendu Ganguly.