Thursday, January 24, 2019
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01/24/2019  4:00pm Let $X_H$ denote the number of copies of a fixed graph $H$ in the random graph $G(n,p)$. Determining the behavior of $X_H$ has long been a central problem in probabilistic combinatorics. Although many results have been established for this random variable, the problem of determining the upper tail of $X_H$ is still an area of active research. In this talk, we examine the case where $H$ is an $l$cycle, showing that
$\mathbb{P}(X_H > (1+\epsilon)E[X_H])<\exp[C_{\epsilon,l}\min\{n^2p^2 \log(1/p),n^lp^l\}]$. Location:
DL 431
