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The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.
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Probability of the random graph on $2n$ vertices having exactly $n$ vertices with degree $\g...
Let $G = (V, E)$ be a uniform random graph on $2n$ labeled vertices and let $S \subseteq {V}$ be the set of vertices with degree $\ge n$. Then what happens to $\mathbf{P}(|S|=n)$ as $n \to \infty$?
Fr …