… to our hypercontractivity theorem, we introduce a new method of localization on high
dimensional expanders of independent interest that enables local-to-global analysis of higher order …

… hypercontractive inequalities on high dimensional expanders. … –Katona theorems for high
dimensional expanders. Our … –Stein decomposition for high dimensional link expanders. …

… hypercontractive inequalities on high dimensional expanders. … – Katona theorems for high
dimensional expanders. Our … –Stein decomposition for high dimensional link expanders. …

… In this work, we develop a new theory of hypercontractivity on high dimensional expanders
(… Unlike previous settings satisfying hypercontractivity, HDX can be asymmetric, sparse, and …

… Using this fact, we prove that high dimensional expanders are reverse hypercontractive, a
powerful functional inequality from discrete analysis implying that for any sets A,B ⊂ X(k), the …

… As applications, we prove an optimal (2 → 4)-hypercontractive inequality for high
dimensional expanders, and a booster theorem for general low influence functions generalizing …

… By instead leveraging the above viewpoint of reverse hypercontractivity as a form of sampling,
we prove any hypergraph X with optimal concentration for degree-i functions in all links12 …

… of high dimensional expansion than we study. Outside of unique games the result has some
further connections to error correcting codes, where approximation algorithms for general …

… highly related to the equivalence of hypercontractivity and small-set … We use decoupling and
hypercontractivity to show tight tail … Motivated by this, we use hypercontractive inequalities to …

We study the computational complexity of approximating the 2-to-q norm of linear operators (defined
as |A| 2->q = max v≠ 0 |Av| q /|v| 2 ) for q > 2, as well as connections between this …