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Hypercontractivity on High Dimensional Expanders: Approximate Efron-Stein Decompositions for $\varepsilon$-Product Spaces
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 …