论文标题
稀疏随机图中引发的4个周期的上尾部问题
The upper tail problem for induced 4-cycles in sparse random graphs
论文作者
论文摘要
在Harel，Mousset和Samotij的突破性论文中，我们解决了集团的上尾问题，我们计算了上尾部的上尾部问题，以供二项式随机图中4个周期的4个周期诱导副本$ g_ {n，p} $。我们观察到一个新的现象在巨大的次级计数理论中。这种现象是，在$ p $的一定（较大）范围内，诱导的4个周期的上尾巴不承认幼稚的平均场近似值。
Building on the techniques from the breakthrough paper of Harel, Mousset and Samotij, which solved the upper tail problem for cliques, we compute the asymptotics of the upper tail for the number of induced copies of the 4-cycle in the binomial random graph $G_{n,p}$. We observe a new phenomenon in the theory of large deviations of subgraph counts. This phenomenon is that, in a certain (large) range of $p$, the upper tail of the induced 4-cycle does not admit a naive mean-field approximation.
