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arXiv · 1005.4471

Upper tails for triangles

Bobby DeMarco·Jeff Kahn
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Abstract

With $ξ$ the number of triangles in the usual (Erdős-Rényi) random graph $G(m,p)$, $p>1/m$ and $η>0$, we show (for some $C_η>0$) $$\Pr(ξ> (1+η)\E ξ) < \exp[-C_η\min{m^2p^2\log(1/p),m^3p^3}].$$ This is tight up to the value of $C_η$.

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Bobby DeMarco, Jeff Kahn. 2011-11-29. Upper tails for triangles. https://doi.org/10.1002/rsa.20382

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