论文标题
有限矢量空间中发病率的阈值功能
Threshold functions for incidence properties in finite vector spaces
论文作者
论文摘要
本文的主要目的是为事件提供阈值函数，即有限矢量空间的点的随机子集具有与点 - 流动性发生率有关的某些属性。具体来说，我们认为事件是有一个$ \ ell $ -rich $ m $ -flat，就$ \ mathbb {f} _q^n $中的一组随机点而言，这一事件是，随机点是$ m $ blocking集，并且在随机的点和随机的积分和随机的$ m $ m $ m $ -m-$ $ -m-$ -m-m-$ -m-m-m-m-lats中都有发生的事件。我们的关键要素之一是Chen和Greenhill（2021）获得的最新结果的更强版本。
The main purpose of this paper is to provide threshold functions for the events that a random subset of the points of a finite vector space has certain properties related to point-flat incidences. Specifically, we consider the events that there is an $\ell$-rich $m$-flat with regard to a random set of points in $\mathbb{F}_q^n$, the event that a random set of points is an $m$-blocking set, and the event that there is an incidence between a random set of points and a random set of $m$-flats. One of our key ingredients is a stronger version of a recent result obtained by Chen and Greenhill (2021).
