高维展开式上的超压缩性：$\varepsilon$ -乘积空间的近似Efron-Stein分解
Hypercontractivity on High Dimensional Expanders: Approximate Efron-Stein Decompositions for $\varepsilon$-Product Spaces
摘要：
证明了高维扩张式上的超压缩不等式。在p偏置超立方体，对称群，和格拉斯曼计划的设置，我们的不等式是有效的整体功能，这是功能，不显着影响的一个小的坐标集的限制。作为应用，我们得到了高维展开式的Fourier集中，小集展开和Kruskal-Katona定理。我们的技术依赖于一个新的近似Efron-Stein分解高维链接扩展。
英文摘要：
We prove hypercontractive inequalities on high dimensional expanders. As in the settings of the p-biased hypercube, the symmetric group, and the Grassmann scheme, our inequalities are effective for global functions, which are functions that are not significantly affected by a restriction of a small set of coordinates. As applications, we obtain Fourier concentration, small-set expansion, and Kruskal-Katona theorems for high dimensional expanders. Our techniques rely on a new approximate Efron-Stein decomposition for high dimensional link expanders.
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