Mei Yin,  University of Denver

Exact asymptotics for constrained exponential random graphs

The unconstrained exponential family of random graphs assumes no prior knowledge of the graph before sampling, but in many situations partial information of the graph is already known beforehand. A natural question to ask is what would be a typical random graph drawn from an exponential model subject to certain constraints? Will there be a similar phase transition phenomenon as that which occurs in the unconstrained exponential model? Using the theory of large deviations, we present some general results for the constrained model and in particular the exact asymptotics for the conditional normalization constant. Part of this talk is based on joint work with Richard Kenyon.