# Mathematics Colloquia and Seminars

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### 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.