The statistical physics of graphs and partition functions represents a vibrant intersection of graph theory, statistical mechanics and computational complexity. By summing over an ensemble of ...

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 for the mean and variance 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 ...

Analogoues of classical representation formulas for entire functions of exponential type are proved in the class of discrete analytic functions. Journal Information This monthly journal, published ...