# On the variational problem for upper tails in sparse random graphs

@article{Lubetzky2017OnTV, title={On the variational problem for upper tails in sparse random graphs}, author={Eyal Lubetzky and Y. Zhao}, journal={Random Struct. Algorithms}, year={2017}, volume={50}, pages={420-436} }

What is the probability that the number of triangles in Gn,p, the Erdi¾?s-Renyi random graph with edge density p, is at least twice its mean? Writing it as exp[-rn,p], already the order of the rate function rn, p was a longstanding open problem when p=o1, finally settled in 2012 by Chatterjee and by DeMarco and Kahn, who independently showed that rn,pi¾?n2p2log1/p for pi¾?lognn; the exact asymptotics of rn, p remained unknown. The following variational problem can be related to this large… CONTINUE READING

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