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Combinatorics Colloquium: The upper tail for triangles in random graphs

Event Type
Altgeld Hall (room # TBD)
May 18, 2022   11:00 am  
Wojciech Samotij, Tel Aviv University
Jozsef Balogh

Abstract: Let $X$ denote the number of triangles in the random graph $G_{n,p}$.  The problem of determining the asymptotics of the logarithimic upper tail probability of $X$, that is, $\log \Pr(X > (1+\delta)\mathbb{E}[X])$, for every fixed positive $\delta$ has attracted considerable attention of both the combinatorics and the probability communities.  We shall present an elementary solution to this problem, obtained recently in a joint work with Matan Harel and Frank Mousset.  The crux of our approach is a simple probabilistic argument, inspired by the work of Janson, Oleszkiewicz and Ruci\’nski, that reduces the estimation of this upper tail probability to a counting problem

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