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Discrete Math

The upper tail for triangles in sparse random graphs

Wojtek Samotij, Tel Aviv

Location:  Hill 705
Date & time: Monday, 05 November 2018 at 2:00PM - 3:00PM


Let X denote the number of triangles in the random graph G(n, p). The problem of determining the asymptotics of the rate of the upper tail of X, that is, the function f_c(n,p) = log Pr(X > (1+c)E[X]), has attracted considerable attention of both the combinatorics and the probability communities. We shall present a proof of the fact that whenever log(n)/n << p << 1, then f_c(n,p) = (r(c)+o(1)) n^2 p^2 log(p) for an explicit function r(c).

This is joint work with Matan Harel and Frank Mousset.

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