We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates ...

Advances in Applied Probability, Vol. 50, No. 1 (2018), pp. 272-301 (30 pages) We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...