广义迁移原理
A generalised transference principle
浏览论文内容
中文总结 AI 辅助
本文提出广义迁移定理，扩展前人结果，用于推导非严格平衡图与超图的稀疏计数引理，在概率p和成功概率上达渐近最优界。
中文摘要 AI 辅助
在过去二十年中，证明组合定理的稀疏随机类似物已成为日益增长的趋势。Conlon与Gowers在《数学年刊》2016年提出的一种统一方法，涉及建立“迁移原理”，该原理可在稠密环境的鲁棒性质与稀疏p-随机环境之间进行转换，前提是p不会过小。本文结果提供了一个更通用的迁移定理，扩展了Conlon和Gowers以及Schacht在《数学年刊》2016年的结果。在众多其他应用中，我们利用该定理得到了不一定严格平衡的图和超图的稀疏计数引理。我们的方法在概率p和成功概率上达到了渐近最优界。
英文摘要
The last two decades have witnessed a growing trend towards proving sparse random analogues of combinatorial theorems. One unified approach to proving such theorems, formalised by Conlon and Gowers [Ann. of Math. 2016], involves establishing a 'transference principle' which allows one to translate between robust properties in the dense setting and the sparse $p$-random setting, provided $p$ is not too small. Our results provide a more general transference theorem, extending the results of Conlon and Gowers and also those of Schacht [Ann. of Math. 2016]. Among a variety of other applications, we use this to obtain a sparse counting lemma for graphs and hypergraphs which are not necessarily strictly balanced. Our method achieves asymptotically optimal bounds on the probability $p$, and the probability of success.
