What is the distribution of the number of triangles in the random graph G(n, 1/2)? It was known for a long time that this distribution obeys a central limit theorem: from the point of view of large intervals (~standard-deviation length), the distribution looks like a Gaussian random variable. We show that it even obeys a LOCAL central limit theorem: the distribution is pointwise close to a suitable discrete Gaussian random variable.
Joint work with Justin Gilmer
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