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The upper tail problem in a random graph asks to estimate the probability that the number of copies of some fixed subgraph in an Erdős‐Rényi random graph exceeds its expectation by some constant factor. There has been much exciting recent progress on this problem. We study the corresponding problem for hypergraphs, for which less is known about the large deviation rate. We present new phenomena in...
The following question is due to Chatterjee and Varadhan (2011). Fix and take , the Erdős‐Rényi random graph with edge density p, conditioned to have at least as many triangles as the typical . Is G close in cut‐distance to a typical
? Via a beautiful new framework for large deviation principles in , Chatterjee and Varadhan gave bounds on the replica...
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