Hypercontractivity on High Dimensional Expanders
PROCEEDINGS OF THE 54TH ANNUAL ACM SIGACT SYMPOSIUM ON THEORY OF COMPUTING (STOC '22)(2022)
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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关键词
hypercontractive inequalities, high dimensional expanders, epsilon-product space, Efron-Stein decomposition, small-set expansion, Kruskal-Katona theorem
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