Hypercontractivity on High Dimensional Expanders: Approximate Efron-Stein Decompositions for ε-Product Spaces [article]

Tom Gur, Noam Lifshitz, Siqi Liu
2021 arXiv   pre-print
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
more » ... ein decomposition for high dimensional link expanders.
arXiv:2111.09375v4 fatcat:pd4s5ihsqjcdvox5sikcrqmaoy