UC Davis Mathematics

Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Concentration of measure in Exponential random graphs

Mathematical Physics & Probability

Speaker: Kyeongsik Nam
Location: 1147 MSB
Start time: Wed, Oct 23 2019, 3:09PM

The exponential random graph model (ERGM) is a central object in the study of clustering properties in network theory 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 regarding spatial mixing properties 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.