Max Hopkins

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20242026

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cs.CC2024

Hypercontractivity on HDX II: Symmetrization and q-Norms

Max Hopkins

Bourgain's symmetrization theorem is a powerful technique reducing boolean analysis on product spaces to the cube. It states that for any product $Ω_{i}^{\otimes d}$ , function $f: Ω_…

cs.CC2024

Chernoff Bounds and Reverse Hypercontractivity on HDX

Yotam Dikstein, Max Hopkins

We prove optimal concentration of measure for lifted functions on high dimensional expanders (HDX). Let $X$ be a $k$ -dimensional HDX. We show for any $i \leq k$ and $f:X(i)\to [0,1]…