对称图性质的乘积测度逼近
Product Measure Approximation of Symmetric Graph Properties
摘要：
在随机结构的研究中，我们经常面临现实性和易处理性之间的权衡，后者通常通过假设某种形式的独立性来实现。在这项工作中，我们开始努力弥合这一差距，通过开发工具，使我们能够与独立的工作，而不假设它。让$\mathcal{G}_{n}$是$n$顶点上的所有图的集合，让$S$是$\mathcal{G}_{n}$的任意子集，例如，具有$m$边的图的集合。对随机网络的研究可以看作是对$S$的大多数元素都适用的性质的研究，即，这对于$S$均匀随机元素是高概率的。考虑到这一点，我们追求以下问题：什么是一般的充分条件的一致措施的一组图$S \subseteq \mathcal{G}_{n}$是近似的产品措施？
英文摘要：
In the study of random structures we often face a trade-off between realism and tractability, the latter typically enabled by assuming some form of independence. In this work we initiate an effort to bridge this gap by developing tools that allow us to work with independence without assuming it. Let $\mathcal{G}_{n}$ be the set of all graphs on $n$ vertices and let $S$ be an arbitrary subset of $\mathcal{G}_{n}$, e.g., the set of graphs with $m$ edges. The study of random networks can be seen as the study of properties that are true for most elements of $S$, i.e., that are true with high probability for a uniformly random element of $S$. With this in mind, we pursue the following question: What are general sufficient conditions for the uniform measure on a set of graphs $S \subseteq \mathcal{G}_{n}$ to be approximable by a product measure?
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
