STOC Conference 2024 Conference Paper
Product Mixing in Compact Lie Groups
- David Ellis
- Guy Kindler
- Noam Lifshitz
- Dor Minzer
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David Ellis
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2STOC Conference 2023 Conference Paper
An Analogue of Bonami's Lemma for Functions on Spaces of Linear Maps, and 2-2 Games
- David Ellis
- Guy Kindler
- Noam Lifshitz
We prove an analogue of Bonami’s (hypercontractive) lemma for complex-valued functions on L (𝑉,𝑊 ), where 𝑉 and 𝑊 are vector spaces over a finite field. This inequality is useful for functions on L (𝑉,𝑊 ) whose ‘generalised influences’ are small, in an appropriate sense. It leads to a significant shortening of the proof of a recent seminal result by Khot, Minzer and Safra that pseudorandom sets in Grassmann graphs have near-perfect expansion, which (in combination with the work of Dinur, Khot, Kindler, Minzer and Safra) implies the 2-2 Games conjecture (the variant, that is, with imperfect completeness)