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

@article{Gur2021HypercontractivityOH, title={Hypercontractivity on High Dimensional Expanders: Approximate Efron-Stein Decompositions for \$\epsilon\$-Product Spaces}, author={Tom Gur and Noam Lifshitz and Siqi Liu}, journal={Electron. Colloquium Comput. Complex.}, year={2021}, volume={TR21} }

Abstract. 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…

## One Citation

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