I’m currently thinking about exponential random graph models (ERGMs) as they appear in mathematics. Traditionally, they are used to model social networks. They can be investigated from a mathematical perspective by asking whether this family of probability distributions satisfy some nice conditions, such as negative dependence. In this way, we connect geometry and probability theory. This connection was described in seminal work by Borcea, Brändén, and Liggett. As part of my PhD candidacy exam, I prepared a document describing this connection with an eye towards ERGMs and quantum field theory.



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